Generalized jet-effect and fluid-repellent corpus

ABSTRACT

The invention provides a method for computational fluid dynamics and apparatuses making enable an efficient implementation and use of an enhanced jet-effect, either the Coanda-jet-effect, the hydrophobic jet-effect, or the waving-jet-effect, triggered by specifically shaped corpuses and tunnels. The method is based on the approaches of the kinetic theory of matter, thermodynamics, and continuum mechanics, providing generalized equations of fluid motion. The method is applicable for slow-flowing as well as fast-flowing real compressible-extendable fluids and enables optimal design of convergent-divergent nozzles, providing for the most efficient jet-thrust. The method can be applied to airfoil shape optimization for bodies flying separately and in a multi-stage cascaded sequence. The method enables apparatuses for electricity harvesting from the fluid heat-energy, providing a positive net-efficiency. The method enables efficient water-harvesting from air. The method enables generators for practical-expedient power harvesting using constructive interference of waves due to the waving jet-effect.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation-in-part of U.S. patentapplication Ser. No. 15/409,876 filed on Jan. 19, 2017, which isincorporated herein by reference in its entirety. This patentapplication is also a continuation-in-part of U.S. patent applicationSer. No. 15/648,469 filed on Jul. 13, 2017, which is incorporated hereinby reference in its entirety.

FIELD OF THE INVENTION

The invention relates generally to fluid dynamics and to use ofjet-effect, applied to headway and oscillating motions in fluids, and,more particularly, to jet-effect modeling and use for either:

-   -   a design of an actually-airfoil profile of a birdlike wing,        and/or    -   a design of an actually-airfoil convergent-divergent jet-nozzle,        and/or    -   an implementation of a hydrophobic jet-gear, and/or    -   an implementation of a gravity-jet engine, and/or    -   an implementation of a sequentially-arranged jet-boosters,        and/or    -   an implementation of constructive interference of acoustic waves        in fluids, wherein the waving jet-effect is further translated        in terms of electromagnetic waves.

The primary teachings of the present invention relate to methods andapparatuses, which are destined for the jet-effect triggering andthereby local acceleration of fluid portions and, in the final analysis,for conversion of the fluid portions warmth into the useful-beneficialpower, either mechanical or electrical; wherein the local accelerationis self-revealing-and-manifesting as either:

-   -   an accelerating headway motion of fluid portions, subjected to        the Coanda-effect and/or the de Laval effect and/or the        hydrophobic jet-effect; and/or    -   an intensified oscillating motion of fluid portions, subjected        to the waving jet-effect resulting in constructive interference        of acoustic waves.

BACKGROUND OF THE INVENTION

The following issued patents and patent publications provide potentiallyrelevant background material, and are all incorporated by reference intheir entirety: U.S. Pat. No. 6,981,366 (Sharpe), US 2008/0061559 A1(Hirshberg), U.S. Pat. No. 8,268,030 (Abramov), U.S. Pat. No. 8,221,514(Abramov), U.S. Pat. No. 8,611,787 (Bulman), US2005/027498 A1 (CANON),US2014/288906 A1 (JAPAN), GB894450 A (GENERAL ELECTRIC), andUS2011/083420 A1 (CLAY).

Preamble and Terminology

The well-known and widely-used jet-effect provides for the effect of gasextension and thereby acceleration. Accelerated flow is widely appliedto propelling some kinds of vehicles having jet-engines usually suppliedby either converging or convergent-divergent nozzles, to which the term“jet-nozzle” is also applied to emphasize the jet-effect importance.U.S. Pat. No. 6,981,366 by Sharpe overviews numerous modifications ofthe jet-effect implementation.

In US 2008/0061559 A1 patent application, Hirshberg points out that thejet-effect is accompanied by decreasing static pressure and temperature,and suggests applying the phenomenon as a trigger for vapor-to-watercondensation.

In U.S. Pat. No. 8,268,030 “Wind Energy Use” and U.S. Pat. No. 8,221,514“Ecologically Clean Method and Apparatus for Water Harvesting from Air”,Abramov points out that a long cascade of streamlined nozzles provides aconvergence of a wider front of fluid flow, and provides for anadaptation of the jet-effect use for big-scale devices.

In this invention, the equation of fluid motion is generalized tocorrespond to the kinetic theory of matter, wherein, in particular, itis shown that a consideration of a fluid, defined as composed ofmolecules in accordance with the kinetic theory of matter, provides forsolving a series of confusing paradoxes, following from the definitions,restricted in the frames of the continuum mechanics.

One of the primary teachings of the present invention, in general, is amethod for computational fluid dynamics and a modeling and optimalimplementation of jet-effect, in particular, including the de Lavaleffect. Optimized jet-boosters, hydrophobic jet-gears, and gravity-jetengines are suggested.

As well, the inventor points out that an acoustic (elastic) wave is aparticular case of the fluid local motion. The inventor takes note thewell-known fact of the constructive and destructive interference ofwaves, when, correspondingly, in-phase and anti-phase portions of wavesare joining. In particular, the joining of two anti-phase waves resultsin the destructive interference seeming as an annihilation of the waves;and the joining of two in-phase waves results in the constructiveinterference thereby forming a cumulative wave characterized by thedouble amplitude and fourfold power. The annihilation and fourfoldpower, both, if not to explain especially, contradict to The EnergyConservation Law.

Analogously, in relation to electromagnetic waves, a commonly knownalternation of constructive and destructive interferences, observed asan alternation of excess and annihilation of the electromagnetic waveenergy, correspondingly, i.e. a seemingly tunnel-like effect, if not toexplain especially, contradicts to The Energy Conservation Law.

There is therefore a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system, either elasticand/or electromagnetic, implementing controllable wave interference,appropriate for use in industry.

A generalized generator, capable of producing the electrical power fromthe wave power increased due to constructive interference of elasticand/or electromagnetic waves, is suggested.

In physics, a wave is an oscillation accompanied by a transfer of energythat travels through a medium (space or mass). Waves consist ofoscillations or vibrations (of a physical quantity), around almost fixedlocations.

Wave motion transfers energy from one point to another, displacingparticles of the transmission medium with little or no associated masstransport. The wave-front propagates in accordance with theHuygens-Fresnel principle saying that every point, which a wave-frontdisturbance reaches, becomes a source of a secondary spherical wave,wherein the interference superposition of these secondary wavesdetermines the form of the wave at any subsequent time. The classicalwave equation is defined as a particular case of the equation of mediummotion, in turn, defined in frames of the continuum mechanics.

For the purposes of the present invention:

-   -   a generalized acoustic wave equation is defined as a particular        case of the equation of molecular fluid motion, generalized to        correspond to the kinetic theory of matter; and    -   generalized electromagnetic wave properties are defined by a        translation of corresponding properties of elastic waves in the        terms of the electrodynamics, basing on justified assumptions        not contradicting to the modern scientific conventions, to        satisfy Maxwell's equations for the electromagnetic field.

For the purposes of the present invention, the generalized term“universe background matter” should be understood in a broad sense, as amatter, which, in principle, presents in all points of space. Namely,the “universe background matter” is a generalized matter comprising atleast a so-called dark matter and neutrino gas.

As well, the inventor points out that the universe is filled with thebackground electromagnetic radiation characterized by the random spatialdistribution of frequencies, amplitudes, phases, polarizations, anddirections of propagation.

Further, referring to the corpuscular theory of electromagneticradiation, and so using the terminology of the kinetic theory of matter,for the purposes of the present invention, the term “electromagneticgas” should be understood as the background electromagnetic radiation.[In quantum mechanics, the term “photon gas” is used.]

The inventor points out to the fact that the magnetic field, inprinciple, if not covered by an exotic hermetic and super-conductiveshell, is spreading through any matter. The magnetic field can belocally compensated by (or strictly speaking, hidden due to) an oppositemagnetic field.

For the purposes of the present invention, the generalized term“universe background energy” should be understood in a broad sense, asan energy, which presents in all points of space. Namely, the “universebackground energy” is an omnipresent generalized energy comprising atleast:

-   -   the so-called dark energy,    -   the heat energy stored in the neutrino gas interpreted in terms        of the kinetic theory of matter,    -   the latent electromagnetic energy, hidden by the so-called        destructive interference, to which the background        electromagnetic radiation is subjected, i.e., in terms of the        kinetic theory of matter, the latent electromagnetic energy is        the internal heat-like energy stored in the “electromagnetic        gas” (the inventor takes note that at least this portion of the        universe background energy interacts with electromagnetic waves        via constructive-destructive interference); and    -   the potential energy stored in the gravitational field.

In relation to the molecular fluid, to analyze the equation of themolecular fluid motion and, in particular, the acoustic wave equation,for the purposes of the present invention, the term “jet-effect” is usedin a wide sense as the effect of fluid flow portion convectiveacceleration at the expense of fluid portion internal heat energy. Inparticular, the jet-effect occurs when the fluid portion moves adjacentto configured walls and is subjected to the walls accelerating action,as seemingly “negative friction”. For example, the fluid is gas and thewalls are configured to form a converging or convergent-divergentnozzle. In particular, the term “jet-effect” is applied to thewell-known and widely-used effect of convective acceleration of awind-portion, which is flowing over a convex upper surface of anairplane wing and is thereby being subjected to the varying of flowfront cross-section in an imaginary convergent-divergent nozzle. Anotherexample is a case, wherein the fluid is water and the configured wallshave a hydrophobic surface. Thus, the term “jet-effect”, used here in awide sense, assumes that the process of gas extension may beinsignificant or latent.

The inventor takes note that, in frames of the classical kinetic theoryof molecular gas, when considering a relatively weak jet-effect (whenthe temperature changes and so-called “black-body radiation” arenegligible), one normally ignores the electromagnetic energy radiationoriginated by the randomly accelerating molecules of ideal gas, assumingthat the radiation, being dominantly hidden due to the destructiveinterference, even though expected to be significant from the energeticpoint of view, is not subjected to the energy conversions substantially.The hidden electromagnetic energy is capable of a manifestation aswell-known phenomena at least such as hydrophilicity, hydrophobicity,magnetism, piezo-electricity, photo-electricity, etc. One can estimatethe hidden electromagnetic energy hypothetically capable of themanifestation. In particular, when considering one-mole portion of amatter composed of Avogadro's number N_(A)≈6×10²³ of moleculesinherently having distributed electrical charges, wherein the Brownianmotion of the molecules results in so-called thermal electromagneticradiation caused by the random superposition of all elemental radiationsthereby resulting in random constructive-destructive interference, thesum radiation power of the portion of matter can be estimated, forinstance, either:

-   -   as the radiation power being higher than the thermal        electromagnetic radiation power by the factor √{square root over        (N_(A))}, when considering a hypothetic assumption of ideally        not-interfering electromagnetic rays of all the orthogonal        radiations (for instance, that all the N_(A) molecules are        moving with regularized accelerations interrelating with        effective velocities, cumulatively, corresponding to the portion        of matter temperature, such that launching elemental radiations        differing in frequency to result in orthogonal frequency        modulation and so not interfering at least at one spatial        point), or, alternatively,    -   as the radiation power being higher than the thermal        electromagnetic radiation power by the factor N_(A), when        considering a hypothetic assumption of ideally-constructive        interference of all the elemental radiations (for instance, that        all the N_(A) molecules are moving in unison with a certain        acceleration interrelating with the effective velocity,        corresponding to the portion of matter temperature, and so are        launching identical elemental radiations to result in        constructive interference of all the originated identical        elemental radiations at least at one spatial point).

For the purposes of the present invention, the term “imaginary wall”,applied to flowing fluid streamlines, should be understood as a material(but not virtual) wall, formed by the fluid's matter, forcedly-borderinga portion of the flowing fluid. I.e. the material but optionallyinvisible by the human eye and thereby imaginary wall acts on adjoiningfluid portions, enforcing the fluid portions to move along thestreamlines, i.e. in alignment with the imaginary wall. When flowingplasma is subjected to an action of a magnetic field, “imaginary walls”are formed by the magnetic field's force-lines defining the streamlinesof the flowing plasma. When considering the electromagnetic field,“imaginary walls” should be understood as formed by the electromagneticfield's force-lines.

The jet-effect is the nature of the well-known Coanda-effect, defined asa tendency of a fluid jetstream to be attracted to and aligned with anearby airfoil surface, i.e. to be specifically accelerated at theexpense of the fluid warmth. For the purposes of the present patentapplication, to emphasize the jet-effect nature of the Coanda-effect,the term “Coanda-jet-effect” is also applied as equivalent to thecommonly known term “Coanda-effect”.

Looking ahead, in relation to the electromagnetic wave equation, for thepurposes of the present invention, in contrast to the term “emptyvacuum”, the term “vacuum” should be understood in the modern sense as“filled” by the universe background matter and by the universebackground energy, and the term “electromagnetic jet-effect” will befurther introduced as having a further extended and specified sense tobe applicable to the electromagnetic field in vacuum.

For the purposes of the present patent application:

-   -   the term “velocity of a flying body” should be understood as the        body motion velocity relative to a stationary fluid; and        vice-versa, the term “flow velocity” should be understood as the        fluid flow velocity relative to the considered body submerged in        the flowing fluid. These two terms are interrelated according to        Galilean relativity;    -   the term “M-velocity” should be understood as the fluid velocity        measured in Mach numbers, or identically, velocity normalized to        the temperature dependent velocity of sound in the fluid; and    -   the well-known terms “low-subsonic”, “high-subsonic”,        “transonic”, “supersonic”, and “hypersonic” are used to specify        the flow velocity ranges as the following;        -   (a) the low-subsonic velocity range is defined as the            M-velocity range comprising M-velocities lower than 0.3            Mach;        -   (b) the high-subsonic velocity range is defined as the            M-velocity range comprising M-velocities higher than 0.3            Mach and lower than 0.8 Mach;        -   (c) the transonic velocity range is defined as the            M-velocity range comprising M-velocities higher than 0.8            Mach and lower than 1.2 Mach;        -   (d) the supersonic velocity range is defined as the            M-velocity range comprising M-velocities higher than 1 Mach            and lower than 5 Mach; and        -   (e) the hypersonic velocity range is defined as the            M-velocity range comprising M-velocities higher than 5 Mach.

Moreover, for the purposes of the present patent application, the term“specific M-velocity” is introduced to separate the terms “lowM-velocities”, associated with M-velocities lower than the specificM-velocity indicated by M*, and “high M-velocities”, associated withM-velocities higher than the specific M-velocity M*. The value of thespecific M-velocity M* will be defined hereinbelow by a specificmolecular structure of fluid. Furthermore, the term “essentialM-velocity range” is defined as an M-velocity range comprising thespecific M-velocity M*.

For the purposes of the present patent application, the term “molecularfluid” should be understood as a fluid substance composed of randomlymoving and interacting molecules, according to the kinetic theory ofmatter. Referring to the defined term “molecular fluid”, the earlierdefined term “flow velocity” is further specified as a measure of themolecular fluid molecules motion in a prevalent direction in addition tothe random Brownian motion.

For instance, air is considered as a molecular fluid, and wind isconsidered as a natural process, bringing fresh portions of air, storingat least both: the heat energy of molecules Brownian random motion andthe kinetic energy of wind motion. Normally, in nature, when the wind isof 10 m/sec, the proportion is such that 99.96% is the heat energy [i.e.warmth] and only 0.04% is the kinetic energy. A phenomenon of atransformation of warmth into a hurricane power is well-known; however,the warmth of ambient natural air remains unused in the world industry.Possession of a technology to control the transformation of thesurrounding air and/or water warmth into a directional motion of thefluid could provide a renewable cycle, comprising:

-   -   transformation of the flowing fluid heat-power into acquired        kinetic-power of an arisen jetstream (and/or into acquired wave        power of an arisen wave);    -   conversion of the jetstream kinetic-power into useful        electric-power; and    -   consumption of the electric-power, in the final analysis,        inevitably dissipating back into the warmth of surrounding        matter.

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system (mechanicand/or electromagnetic), implementing a controllable jet-effect (theCoanda-jet-effect and/or the electromagnetic jet-effect,correspondingly) appropriate for use in industry.

The Origin of Life

The term “chiral”, applied to a body, has a sense that the body has anoverall shape, asymmetric in such a way that the shape and its mirrorimage are not superimposable. Reference is now made to prior art FIG. 1a, showing schematically a so-called “left-handed” stereoisomer of anamino acid molecule, marked by numeral 1, being chiral, i.e. there isanother so-called “right-handed” stereoisomer, marked by numeral 2, inreality or in potential, that is of identical composition, but which isarranged in a non-superimposable mirror image configuration.

The spatial chiral property defines a complementarity. For instance, abolt and hex nut are complementary when the both have the same chiralscrew. As well, for instance, it is well-known a helical antenna that isan antenna consisting of a conducting wire screwed in the form of achiral helix. The chiral helix in the antenna can twist in two possibledirections: right-handed or left-handed, as defined by the right-handrule. In an axial-mode helical antenna, the direction of twist of thehelix determines the polarization of radio waves: a chiral left-handedhelix radiates chiral left-circularly-polarized radio waves, while achiral right-handed helix radiates chiral right-circularly-polarizedradio waves. When receiving circularly polarized signals, the chiralhandedness of the receiving antenna must be the same as the transmittingantenna; chiral left-hand polarized antennas suffer a severe loss ofgain when receiving chiral right-circularly-polarized signals, and viceversa.

A definition of life is neither simple nor unequivocal in the nowadayscience. One qualifies a life as an existence of matter in a form ofself-replicating protein molecules, or more fundamentally, ofribonucleic acid (RNA) molecules. However, the origin of life remains anextraordinary problem. The principle question about the origin of lifeis the following. What is the origin of the dominant presence ofleft-handed stereoisomers of amino acids in the live-nature on theEarth, even though their synthesis normally results in an equal mixtureof the right- and left-handed molecular forms? Innumerable mechanismshave been proposed for the origin of left-chiral dominance in aminoacids, and none has been proven.

There is, therefore, a need in the art for a method to provide a properpossible natural mechanism allowing for a synthesis of long spiral-likemolecules, composed of a certain kind of stereoisomers of amino acidsonly.

Venturi Effect

Reference is now made to prior art FIG. 1b . FIG. 1b is a schematicillustration of an airfoil-shaped convergent-divergent nozzle 102,pipe-section in a sagittal plane. The shape can be described ascomprising an inlet part 103 constricting into a narrow throat 104,further followed by a divergent outlet part 105. When a fluid 106 flowsslowly through convergent-divergent nozzle 102, a jet-effect is observedin an adiabatic process, i.e. velocity increases in narrow throat 104 atthe expense of the static pressure in fluid 106. Speedometers 1071,1072, 1073 and barometers 1081, 1082, 1083 illustrate the interrelatedbehavior of the velocity and static pressure. This jet-effect is knownalso as the Venturi effect. Thus, the Venturi acceleration effect isobserved in the case of a slow and converging flow, and the Venturiretarding effect is observed in the case of a slow and divergent flow.

The inventor points out and emphasizes that the phenomenon of theVenturi effect is the self-acceleration and self-retarding of an airflowportion, i.e. is the airflow velocity self-oscillation, at the expenseof the air portion's warmth. I.e., in other words, the Venturi effect ofthe airflow velocity self-oscillation (as well as the Coanda-jet-effect)has the jet-effect nature.

When observing a freely falling water jetstream, one explains a conicconstriction of the water jetstream by the Venturi effect, where theaccelerated jetstream becomes accompanied by a decrease of thecross-sectional area.

Reference is now made again to prior art FIG. 1b , wherein now, all theshaped walls are made from a conductive material, for simplicity, from ahypothetic super-conductor. When an electric flux of the electric field106 flows through convergent-divergent nozzle 102, comprising inlet part103, narrow throat 104, and outlet part 105, a Venturi-like effect,applied to the electric field, is observed in an adiabatic process.Namely, the electric flux, indicated by Φ, is defined as Φ=AE_(A), whereA is the cross-sectional area and E_(A) is the electric field, measuredin the cross-sectional plane. The equation of continuity, applied to theelectric flux, says that Φ₁₀₃=Φ₁₀₄=Φ₁₀₅, i.e.A₁₀₃E₁₀₃=A₁₀₄E₁₀₄=A₁₀₅E₁₀₅, where indexes “103”, “104”, and “105” relateto inlet part 103, narrow throat 104, and outlet part 105,correspondingly. This means that the electric field E₁₀₄ in narrowthroat 104, is higher than the electric field E₁₀₃ in inlet part 103 andhigher than the electric field E₁₀₅ in outlet part 105. The energy U_(E)of electric flux crossing the frontal area A is defined asU_(E)=0.5Aε|E_(A) ²|=0.5εE_(A)Φ, where ε is dielectric constant.Comparing the electric field energy U_(E103)=0.5A₁₀₃ε|E₁₀₃ ²|,U_(E104)=0.5A₁₀₄ε|E₁₀₄ ²|, and U_(E105)=0.5A₁₀₅ε|E₁₀₅ ²|, relating toinlet part 103, narrow throat 104, and outlet part 105, correspondingly,one confusingly discloses that the electric field energy is notconstant, namely, the field energy U_(E104) is higher than the fieldenergies U_(E103) and U_(E105).

Looking ahead, the Venturi-like effect, applied to the electric andmagnetic fields, will be explained and conceptually embodied in thepresent invention. It will be shown that the Venturi-like effect appliedto electric or magnetic field has a fundamental sense in electromagneticwaves propagation and interference.

De Laval Effect

Reference is now made to prior art FIGS. 1c and 1d . FIG. 1c showsschematically a pipe 100 referred to the de Laval nozzle that, inprinciple, is similar to pipe 102 shown in FIG. 1b , but now theincoming fluid-flow 101 is sufficiently fast such that fluid 101 becomessubstantially compressible-expandable. In this case, in an adiabaticprocess, the de Laval effect is observed. This is the effect ofextension of fluid 101 in the divergent outlet part 142 resulting in afurther decrease of the static pressure and temperature and a correlatedincrease of the flow velocity.

FIG. 1d illustrates schematically graphics of distributions of thefluid-flow 101's (FIG. 1c ) three parameters: velocity 150, staticpressure 160, and temperature 170, each along the length of nozzle 100.A standard rocket convergent-divergent jet-nozzle 100 can be modeled asa cylinder 140 that leads to a constriction 141, known as the “throat”,which leads into a widening “exhaust bell” 142 open at the end. Thelocation of the narrowest cross-section of the throat is called as the“critical condition” point 180. High speed and thereforecompressible-expandable hot fluid 101 flows through throat 141, wherethe velocity picks up 151 and the pressure and temperature fall, 161 and171 correspondingly. Hot fluid 101 exits throat 141 and enters thewidening exhaust bell 142. It expands rapidly, and this expansion drivesthe velocity up 152, while the pressure and temperature continue tofall, 162 and 172 correspondingly. This jet-effect phenomenon of fluid101 extra-acceleration at the expense of the fluid 101 heat energy,defined by the static pressure, temperature, and density, is applied tojet-engines, particularly to accelerate a rocket. A sharp slope of thestatic pressure, observed in throat 141, results in pressure waves,called Mach waves. An undesired influence of the Mach waves in the deLaval nozzle is described, for example, in U.S. Pat. No. 8,611,787“Rocket nozzles for unconventional vehicles” by Bulman.

Looking ahead, the enhanced jet-effects: the de Laval jet-effect and thede Laval retarding-effect, both will be conceptually embodied in thepresent invention.

Ordinary Blowing Ventilator

FIG. 1e is a prior art schematic drawing of ordinary blowing ventilator110 operating in open air space. Ordinary blowing ventilator 110,defined by the main functionality to launch a jetstream characterized bythe flow headway-motion kinetic-power, has an inherent engine [not shownhere] consuming either a power of burned fuel or an electrical power.Ordinary blowing ventilator 110 comprises blades 112, having anasymmetrical shape such that, when forcedly rotating in frontal plane119 and covering effective cross-section 114, suck air portions 115.Afrom space “A1” located upstream-afore effective cross-section 114 andconvert air portions 115.A into an accelerated jetstream 115.B enteringspace “B1” located downstream-behind effective cross-section 114. Space“A1”, comprising air portions 115.A subjected to the sucking and motionthrough effective cross-section 114, is bordered by streamlines, formingimaginary contours 116.A. The imaginary contours 116.A separate space“A1” from space “C1”, comprising air portions 115.C, drawn by moving airportions 115.A and flowing toward frontal plane 119 out of effectivecross-section 114. Space “B1”, comprising jetstream 115.B, is borderedby streamlines, forming imaginary contours 116.B. The imaginary contours116.B separate space “B1” from space “D1”, comprising air portions115.D, drawn by jetstream 115.B and flowing downstream-behind frontalplane 119. A complicated motion of air portions 115.A, 115.B, 115.C, and115.D comprises both: a headway-motion, i.e. a laminar component ofmotion aligned with the imaginary contours 116.A and 116.B having aprevalent direction along imaginary sagittal axis 111, and awhirling-motion, i.e. a turbulent component of motion, dominantly,whirling around imaginary sagittal axis 111. For the purposes of thepresent patent application, the term “sagittal axis” is applied to anaxis co-directed with a prevalent direction of a flow headway motion.The mentioned term “streamlines”, applied to imaginary contours 116.Aand 116.B, has a widened sense, spread to the streamlines projections ona plane comprising imaginary sagittal axis 111, for instance, eithersagittal or transversal, meaning that there is no essential massexchange between:

-   -   air portions 115.A of space “A1” and air portions 115.C of space        “C1”, and    -   helically whirling jetstream 115.B of space “B1” and air        portions 115.D of space “D1”.        The power, consumed by ordinary blowing ventilator 110 is        expended for:    -   the complicated motion of air portions 115.A, which then are        transformed into helically whirling jetstream 115.B;    -   the complicated motion of air portions 115.C, which then are        transformed into moving air portions 115.D;    -   the overcoming of air viscous-resistance; and    -   the compensation of inner resistance of the inherent engine.        Wherein the part of the power consumption, expended for the        overcoming of air viscous-resistance and compensation of inner        resistance of the inherent engine, dissipates in the acquired        warmth of outflowing air portions 115.B and 115.D.        Streamlines 116.A and 116.B constitute an imaginary        convergent-divergent tunnel, where, in addition to the mentioned        effect of flow complicated motion, powered by forcedly rotating        blades 112, the Venturi effect, described above referring to        FIG. 1b , occurring in an adiabatic process, is expected,        thereby saving the power for the additionally acquired        convective acceleration of jetstream 115.B. The velocity of        jetstream 115.B headway-motion is distributed on cross-section        118 non-uniformly. Shapes of forcedly rotating blades 112, on        the one hand, define the shapes of imaginary contours 116.A and        116.B, and on the other hand, define the jetstream 115.B        headway-motion velocity distribution on cross-section 118. The        resulting functionality net-efficiency of ordinary blowing        ventilator 110 is defined by the ratio of the kinetic-power of        launched jetstream 115.B headway-motion to the power, consumed        by the inherent engine of ordinary blowing ventilator 110.        Taking into the account the mentioned Venturi effect, the        resulting net-efficiency of ordinary blowing ventilator 110        interrelates with the Venturi effect efficiency.

The inventor points out and emphasizes that whereas the functionalitynet-efficiency of a blowing ventilator is provided, in particular, dueto the Coanda-jet-effect, i.e. at the expense of ambient warmth,conditions, when the net-efficiency becomes higher than 100%, are notexcluded. Looking ahead, in view of the description referring to FIGS.7e and 7f of the invention, it will be evident to a person studied theinvention, that such conditions are specified.

Phenomenon of Convective Self-Acceleration

FIG. 1f is a prior art schematic drawing of a body 12.0 blown by aninitially laminar airflow having portion 12.2 enveloping body 12.0. Itis assumed that a velocity of the airflow motion is much lower than 0.5Mach, for instance, 1 m/sec. For simplicity and without loss ofreasoning, consider a case when the body 12.0 corpus has at leastpartially airfoil shape providing for that ambient-adjoiningsub-portions 12.5 and 12.6 of airflow portion 12.2 remain laminar atleast upstream afore a frontal plane, crossing the body 12.0 corpus.

Here,

-   -   such a frontal plane is marked with the dotted line having        numeral 12.1;    -   dashed lines 12.3 and 12.4 are imaginary streamlines bordering        airflow portion 12.2 as a whole and being sufficiently far from        body 12.0 that allows to ignore the airflow streamlines minor        curving when bordering ambient-adjoining sub-portions 12.5 and        12.6; and    -   arrow 12.7 symbolizes a portion of downstream airflow, not        obligatorily laminar.

When flowing around body 12.0, ambient-adjoining sub-portions 12.5 and12.6 of airflow portion 12.2 become subjected to reshaping and can beconsidered as moving through an imaginary tunnel, which is characterizedby varying cross-sectional area. According to the mass conservation law,called also the equation of continuity: Aρu=Const, where ρ is thedensity of flux; u is the flux velocity, and A is the fluxcross-sectional area, ambient-adjoining sub-portions 12.5 and 12.6 movefaster than yet to be reshaped airflow portion 12.2 because the airdensity changes are minor at low airflow velocities and the sub-portionshave the cumulative cross-sectional area smaller than thecross-sectional area of yet to be reshaped airflow portion 12.2.Therefore, the cumulative kinetic energy of ambient-adjoiningsub-portions 12.5 and 12.6 is higher than the kinetic energy of oncomingairflow portion 12.2 yet to be subjected to the reshaping.

One of the key questions about the origin of flowing fluid portionacceleration is the following. At the expense of what kind of energy thesub-portions became accelerated, if the case is adiabatic? The answer tothe question is the self-acceleration occurs at the expense of theinternal heat energy of the flowing fluid portion itself, wherein theinitial velocity of the flowing fluid portion plays a role of a“trigger-catalyst” defining an intensity of the self-acceleration,namely, a higher velocity results in a greater self-acceleration. Theanswer shows that the phenomenon of convective self-acceleration isinevitable for fluid flowing around a body with relatively lowvelocities in an adiabatic process, i.e. upon conditions usuallyprovided in the actual practice.

The inventor points out and emphasizes that a portion of the flowingfluid may play the role of a body subjected to a blowing by anotherportion of the flowing fluid—this situation occurs, for instance, inacoustic waves.

Reference is now made again to prior art FIG. 1f , wherein now, theairfoil body 12.0 has a conductive shell, or, for simplicity, a shellmade from a hypothetic super-conductor. When the electric flux Φ_(12.2),indicated by numeral 12.2, flows around body 12.0, a Venturi-like effectapplied to the electric field is observed in an adiabatic process.

Namely, when flowing around body 12.0, ambient-adjoining sub-portionsΦ_(12.5), indicated by numeral 12.5, and Φ_(12.6), indicated by numeral12.6, of the electric flux Φ_(12.2) become subjected to reshaping andcan be considered as flowing through an imaginary tunnel, which ischaracterized by varying cross-sectional area. According to the equationof continuity: Φ=AE_(A)=Const, where Φ is the electric flux, A is thecross-sectional area, and E_(A) is the effective electric field,measured in the cross-sectional plane, the ambient-adjoiningsub-portions Φ_(12.5) and Φ_(12.6) of electric flux Φ_(12.2) arecharacterized by electric fields E_(12.5) and E_(12.6), both (and hence,the weighted average effective electric field) being higher than theelectric field E_(12.2) of yet to be reshaped electric flux Φ_(12.2),i.e. E_(12.5)>E_(12.2) and E_(12.6)>E_(12.2), because the sub-portionshave the cumulative cross-sectional area smaller than thecross-sectional area of yet to be reshaped flux Φ_(12.2). As the energyU_(E) of electric flux crossing the frontal area A is defined asU_(E)=0.5Aε|E_(A) ²|=0.5εE_(A)Φ, where ε is dielectric constant,therefore, the electric energy of ambient-adjoining sub-portions 12.5and 12.6 is higher than the electric energy of original flux 12.2 yet tobe subjected to the reshaping.

Again, one of the key questions about the origin of the electric energyself-increase is the following. At the expense of what kind of energythe sub-portions became of higher energy if the case is adiabatic? Theinevitable answer to the question is the self-increase occurs at theexpense of the universe background energy (at least at the expense ofthe latent electromagnetic energy) stored in the space occupied by theelectric flux itself, wherein the initial electric field of the fluxplays the role of a “trigger-catalyst” defining an intensity of theself-increase, namely, a higher electric field results in a greaterself-increase. The answer shows that the phenomenon of self-increase isinevitable for flux flowing around a conductive corpus in an adiabaticprocess, i.e. upon conditions usually provided in the actual practice.

Seeing the similarity of behaviors:

-   -   on the one hand, of fluid flow flowing around an airfoil body        having a mechanical shell, and,    -   on the other hand, of electric flux flowing around an airfoil        body having a conductive shell,        for the purposes of the present invention, analogously to the        Coanda-jet-effect, the term “electromagnetic jet-effect” is        defined as a tendency of an electric field to be attracted to        and aligned with a surface, capable of an interaction with the        electric field, for instance, a conductive surface, wherein the        tendency is accompanied by the electric field to be specifically        increased at the expense of the universe background energy (at        least at the expense of the latent electromagnetic energy).        Airfoil Wing

FIG. 1g is a prior art schematic drawing of a classic airfoil profile ofan airplane wing 10 in a sagittal plane. The wing profile isrecognizable by a rounded leading edge, a convex profile contour, havingsmoothly curved, elongated sides: more convex and lesser convex, and asharp trailing end. A horizontal oncoming air stream 12 runs on therounded leading edge and flows around wing 10, thereby being dividedinto two laminarly moving portions: upper air flux 14 and lower air flux15, both stalling at the sharp trailing end. The axis 11 of wing 10 isdefined as separating the upper and lower fluxes. Axis 11 of wing 10 andthe horizontal direction of oncoming air stream 12 constitute aso-called “attack angle” 13. The more convex upper side provides aslippery surface, and the lesser convex lower side, exposed to oncomingair stream 12 with attack angle 13, and so subjected to an impact bylower air flux 15, has thereby more frictional-dragging surface. TheCoanda-effect is defined as a tendency of a fluid jetstream to beattracted to and aligned with a nearby airfoil surface. The well-knownlift-effect of an airplane wing 10 arises due to the non-symmetricalprofile of wing 10 when the upper side is more convex. Firstly, alift-force is defined by attack angle 13, which redirects the flowingwind. Secondly, when attack angle 13 is equal to zero, wing 10, havingan ideally streamlined contour, provides that the sliding upper air flux14 and the impacting lower air flux 15, both subjected to theCoanda-effect operation, meet behind wing 10. Sliding upper air flux 14and impacting lower air flux 15, flowing around wing 10, incur changesin their cross-sectional areas and are accelerated convectivelyaccording to the mass conservation law. Considering relatively lowvelocities, the varying cross-sectional areas result in that the slidingupper air flux 14 runs faster than the impacting lower flux 15.According to Bernoulli's principle, this results in less so-calledstatic pressure on wing 10 from sliding upper flux 14 than the staticpressure from the impacting lower flux 15. If upper flux 14 and lowerflux 15 flow around wing 10 laminarly, the difference of the staticpressures is defined as ΔP=C_(d)ρu²/2, where ΔP is the static pressuredifference defining the lift-force, in particular, when attack angle 13is equal to zero, C_(d) is the coefficient, depending on wing 10'snon-symmetrical profile, p is the density of the air; and u is thevelocity of the ambient airflow relative to wing 10. A wing, having anelaborated airfoil profile, provides for a gradual variation of theairflow static pressure along the profile's smoothly curved contour and,when flying with a certain velocity, results in a linear change of theairflow static pressure along the profile's smoothly curved contour,thereby satisfying a condition preventing an origination of turbulences.In practice, there are also turbulences and vortices of the fluxes,which are not shown here. The prevalent flows, turbulences and vorticesresult in a spatial distribution of the air static pressure,particularly, in a local static pressure reduction and local extensionsof the flowing air. Consider an air portion flowing around wing 10,referring to the Clapeyron-Mendeleev law concerning a so-calledhypothetical ideal gas state: P=ρR₀T/μ, where P is the gas staticpressure, ρ is the gas density, T is the absolute temperature of thegas, μ is the gas molar mass, and R₀ is the universal gas constant. Onecould apply rough and more exact explanations for changes in the gasstate parameters of the air portion flowing around wing 10.

Roughly, for the sake of estimation of a relatively slow wind tendencyonly, considering the flowing air as substantially incompressible gas,Gay-Lussac's law for an isochoric process interrelates the staticpressure P and absolute temperature T by the equation ΔP/P=ΔT/T, i.e.the reducing static pressure is accompanied by the decreasing absolutetemperature.

More exactly, for the wind at slow speeds as well as at higher speedsrunning, in general, at a non-zero attack angle 13, the air, beingcompressible-expandable as an ideal gas, flowing around wing 10,performs work W for the air portion volume extension, wherein the volumeextension process is substantially adiabatic. The adiabatic extensionresults in a change of the portion of gas internal energy, accompaniedby a static pressure reduction and temperature decrease. The work Wperformed by the wind portion of 1 mole flowing around wing 10 for theadiabatic process is defined as: W=C_(V)ΔT_(a), where C_(V) is the molarheat capacity for an isochoric process, and ΔT_(a) is the adiabatictemperature decrease of the considered air portion. The value of theadiabatic temperature decrease ΔT_(a)=T₂−T₁ is bonded with staticpressure reduction by the relation: T₂/T₁=(P₂/P₁)^((j-1)/j), where P₁and P₂ are the static pressures of the subject air portion before andafter the adiabatic process correspondingly, and j is the adiabaticcompressibility-constant, which is defined by molecular structure ofgas, wherein the value j=7/5 is a good approximation for natural air asconsisting dominantly of diatomic molecules. So, considering relativelylow velocities, the Coanda-effect, occurring upon the convex side ofwing 10, is accompanied by a kind of jet-effect, i.e. is accompanied byan observed acceleration of a wind portion and by the wind portion'sstatic pressure and temperature decrease. Thus, the Coanda-effect andlift-effect are interrelated self-revealing-and-manifestations of thetriggered jet-effect.

A well-known phenomenon of upper flux 14 adiabatic cooling atlow-subsonic velocities is observed. Natural air is humid, and the localcooling, accompanied by the pressure reduction, acts, in particular, asa water condensation trigger. If the wind flows around a wing with anM-velocity equal to or higher than the Mach number (i.e. the speed ofsound), a well-known phenomenon of shock sound-wave emission takesplace. This shock sound-wave is not caused by wing vibration, but ariseswhen myriad of acoustic waves become in-phase superposed thereby formingthe resonance resulting in the shock sound-wave; moreover, it becomesevident that the shock sound-wave is originated at the expense of theinternal heat energy of air and so is accompanied by the air temperatureshock decrease, provoking the process of vapor condensation intowater-aerosols.

FIG. 1h is a prior art schematic drawing of considerable amounts ofwater-vapor condense into water-aerosols 16.1 and sublimate intomicro-flakes-of-snow 16.2, which are observed behind the high-speedaircraft's 16 wings' nozzles. One could note that the effect occurs atflow speeds substantially lower than the Mach number, i.e. it is nottriggered by the mentioned phenomenon of shock sound-wave emission. Thisphenomenon explanation cannot be derived from the classical equations offluid motion, predicting the extra-decrease of static pressure andtemperature at transonic and supersonic velocities only. On the otherhand, air-fluxes, which flow nearby around a body, become warmer andextra-warmed, when the body flies in air-environment with transonic,supersonic, and/or hypersonic velocities. A correct prediction ofthermodynamic effects occurred in fluid flowing around a wing wouldprovide an improved design of a wing shape to control and optimize thelift-effect.

There is, therefore, a need in the art for a method and apparatus toprovide a correct optimal design of the wing shape to reach the mostefficient and controlled lift-effect.

Point of Sail

The term “point of sail” is used to describe a sailing boat orientationwith respect to a prevalent direction of the ambient wind.

Prior art FIG. 1i is a schematic illustration of points of sail. Asailboat exposed to ambient wind 18.0 in positions and orientations:18.1, 18.3, 18.5, 18.6, 18.7, 18.9, 18.11, and 18.12 with respect to theprevalent direction of ambient wind 18.0 is shown schematically. Thepositions and orientations of the sailboat, i.e. the points of sail, areclassified by groups, indicated by symbols “A”, “B”, “C”, “D”, and “E”.Group “A” is so-called “in irons” (into the wind) or “no-go zone”, group“B” is so-called “close-hauled”, group “C” is so-called “beam reach”,group “D” is so-called “broad reach”, and group “E” is so-called“running”.

A sailboat is a well-known example, showing that a passive sail, playinga role of a trivial nozzle, enables to move the sailboat at leastpartially in the upstream direction against ambient wind 18.0, forinstance along a zigzag path. In other words, in fact, the passive sailexposed to ambient wind 18.0 produces “a net jet-thrust” against ambientwind 18.0. In simple words, in fact, the ambient wind 18.0 sucks thepassive sail but not pushes it. Shaded sector 18.2 corresponds to the“no-go zone”, where the single passive sail, being in position andorientation 18.12 belonging to point of sail group “A”, does not providea net jet-thrust in the upstream direction against ambient wind 18.0.

Point of sail “B”, called also “B”-point of sail, having the sailboatposition and orientation 18.1, is shown also in enlarged view 18.Streamlines 18.13 show a windward wind flow aligned with the concaveside of sail; streamlines 18.14 show a leeward wind flow subjected tothe Coanda-effect and so moving along a curved trajectory adjoining theconvex side of sail; a multiplicity of arrows 18.15 indicate“lift-forces”, in this case, directed horizontally, caused by thedifference between static pressures at the concave and convex sides ofsail; and arrow 18.16 indicates a portion of wind acceleratedconvectively, i.e. at the expense of the internal heat energy of wind.The convectively accelerated wind portion 18.16 acts on the sailboat byreactive force 18.17 according to Newton's Third Law. Reactive force18.17 is vectored in the upstream direction. While lift-forces 18.15become compensated dominantly by a stabilizing reaction of thesailboat's keel, which is not shown here, the reactive force 18.17defines the sailboat headway motion primarily.

The effect of net jet-thrust against ambient wind is a kind ofjet-effect; i.e. it is the effect of convective acceleration of a windportion flowing along a curved trajectory adjoining the convex side ofpassive sail in point of sail “B” due to the Coanda-jet-effect, and inturn, the accelerated wind portion causes the net jet-thrust, accordingto Newton's Third Law. To move against the wind, the sail, characterizedby point of sail “B” and orientation 18.1, must extract from the air theinternal heat power, associated with the arisen reactive force 18.17,higher than the mechanical power of the oncoming wind 18.0 blowing thesail downstream away. In this case, one observes that the“drag-in-the-direct-sense”, determined by the cumulative resistance ofthe sailboat to the oncoming airflow due to the sailboat non-zerofrontal cross-sectional area and due to the effect of so-calledskin-friction, is weaker than the seemingly “negative drag”, determinedby the jet-thrust.

The inventor takes note that, when tracing after a wind portion withrespect to a system of coordinates linked with the wind portion yet tobe accelerated due to the Coanda-jet-effect operation, one interpretsthe mentioned wind portion local acceleration as a peculiar shock-likewave propagating downstream, backward with respect to the headway motionof the sailboat.

For the purposes of the present invention, the introduced term “peculiarshock-like wave” should be understood as a fluid reaction originated bya local acceleration of a fluid portion in a prevalent direction.

In view of the foregoing description referring to prior art FIG. 1i , itwill be evident to a person skilled in the art that two sailboats, bothbeing positioned in “B”-point of sail, wherein one of the sailboats hasposition and orientation 18.1 and the other sailboat has position andorientation 18.11, when connected and consolidated together and therebyaggregated as a whole, provide a condition for a resultant netjet-thrust applied to the aggregation, directed straight against ambientwind 18.0. In this case, the ambient wind 18.0 just sucks the passivepair of sailboats.

The inventor points out and emphasizes that the phenomenon of netjet-thrust of sail in point of sail “B” occurs due to theself-acceleration of an airflow portion at the expense of the airportion's warmth. I.e., in other words, the net jet-thrust of sail inpoint of sail “B” occurs due the Coanda-jet-effect.

In spite of the fact that the effect of net jet-thrust against theambient wind is widely used in cruising on water, the effect remainsunused in the world industry.

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system, implementingthe kind of jet-effect providing the net thrust in the upstreamdirection, for a controllable use in industry.

Flying Bird

For the purposes of the present patent application, the inventor pointsout to a flying bird, to take note that the jet-effect is not so exotic,to emphasize the jet-effect potential efficiency, and to make clear thatthe Coanda-jet-effect is one of the primary and quintessential aspectsof the present patent application. The inventor points out that a flyingbird makes waving motions rather than rowing or pushing off motions byits wings. The waving can be interpreted as a booster of theCoanda-jet-effect as well as a source of forced elastic waves. Theinventor points out to a flying bird, the wings waving of which is notso frequent but nevertheless is enviably efficient. In particular for apigeon, while the wings waving velocity with respect to the bird body isabout 1 m/sec only, the bird flying-acceleration in a horizontaldirection up to seemingly-paradoxical high velocities, higher than 10m/sec (actually, higher than 30 m/sec and even 40 m/sec), becomesreachable;—it confirms that the primary mechanism of theflying-acceleration is at least not the pushing off in the direct sense.

For a comparison, a flying relatively large bird, for instance, agolden-eagle, and a running cheetah, both overcome the air drag andsupport the upward and downward mobility (wherein the cheetah's verticalmobility is defined by a ground relief and small jumps of the cheetah'scenter of mass only). For simplicity of the comparison, ignore thesidelong (leftward and rightward) mobility. The flying golden-eagle,“pushing off” gaseous air (take note, the “pushing off” is notintensively-frequent), overcomes the air drag and supports the upwardand downward mobility much easier and moves in the horizontal directionmuch faster, than the running cheetah pushing off a solid surface,wherein pushing off substantially more intensive-frequently providingfor a velocity of paws with respect to cheetah's body being equal to thevelocity of cheetah. At the first glance, this fact looks as mystery andconfusingly-paradoxical. However, it becomes easily-explainable, if notto ignore the triggered Coanda-jet-effect as for the lift-force as wellas for the forward motion acceleration (analogously as the netjet-thrust in the aforementioned example with the sailboat in “B”-pointof sail described with the reference to FIG. 1i ). I.e. it becomeseasily-explainable if the bird wing is interpreted as a sail orientedhorizontally as “B”-point of sail to provide an upward-and-forwardjet-thrust as seemingly “negative drag”. In spite of the fact, that theefficiency of net jet-thrust of the flying bird is attractively high,the phenomenon remains unused in the world industry.

Furthermore, a style of a flock of cranes flying is well-known. Thestyle combines waving of wings, when the flying is accelerating, as wellas wings gliding, when the flying is stabilized. This style promptsthat:

-   -   on the one hand, there are no turbulent vortices behind the        gliding wings of the flying cranes and so the previous gliding        crane does not hinder but even helps to the next gliding crane        in lift and in jet-thrust; and    -   on the other hand, there is an interference of omnidirectional        waves generated by the waving wings of the cranes of flock,        thus, it is self-suggested the assumption that the flying cranes        use the constructive interference thereby helping to each other        in the waving-itself.        In spite of the fact that the cranes apply the cascaded        multi-stage repeating and thereby reinforcing the        Coanda-jet-effect for originating both: the lift-force and the        net jet-thrust during a long time, this technique remains unused        in the world industry.

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system implementingthe repeatedly reinforced Coanda-jet-effect of laminar moving fluid aswell as the repeatedly reinforced constructive interference of waves inthe fluid, both providing the scalable and controllable use of theacquired power in the industry.

In view of the foregoing description of subparagraph “Phenomenon ofConvective Self-Acceleration” with the reference to prior art FIG. 1f ,subparagraph “Airfoil Wing” with the reference to prior art FIG. 1g ,and subparagraphs “Point of Sail” and “Flying Bird”, both with thereference to prior art FIG. 1i , it will be evident to a person skilledin the art that:

-   -   Regarding the well-known “ground-effect”, in contrast to the        well-known effect of proportional interrelation between the        lift-force and drag-force predicted for alone classic wing        flying in a free space, the “ground-effect”, at the first glance        characterized by a confusingly-paradoxical interrelation between        the lift-force and drag-force, namely, by the increased        lift-force and decreased aerodynamic drag (seemingly negative        friction), becomes explainable if one takes into account that,        when the classic wing is moving above and nearby a flat surface        of ground, a boosting of the Coanda-jet-effect upon the convex        upper surface of the wing is expected, and, as a result, the        additional lift-force in the vertical direction and the        additional net jet-thrust in the horizontal direction, both are        acquired due to the Coanda-jet-effect boosting; wherein the        seemingly aerodynamic drag reduction, actually, is the        additional net jet-thrust acquired due to the boosted        Coanda-jet-effect; and    -   Regarding the well-known Gray's paradox in relation to a dolphin        high-speed swimming, saying that, considering the water viscous        resistance and the dolphin's potential muscle power, the dolphin        swimming with the velocity ten times higher than expected is        confusingly-paradoxical, the Gray's paradox becomes solvable if,        in addition to the dolphin muscle power, one takes into account:    -   the dolphin epidermis hydrophobicity, resulting in a reduction        of the viscous skin-friction providing a so-called “free-slip”        condition of motion, and especially,    -   the dolphin body airfoil shape forming “B”-point of sail,        resulting in the net jet-thrust interrelated with the water        portions local acceleration (accompanied by the backward        peculiar shock-like and forced waves) originated due to the        Coanda-jet-effect (i.e. at the expense of the ambient water        warmth) which becomes triggered when the dolphin headway motion        is accompanied by the dolphin's body waving.        The inventor points out that the mentioned tenfold increase in        velocity corresponds to the increase in power by the factor        of 1000. This says that the combination of hydrophobicity,        shaping of a body, and a waving motion may become the        primary-decisive mechanism of motion that will be shown        hereinafter in the description referring to FIGS. 5c, 5d, 5f,        5g, 5h, 5i, 5j , and 5 k.        Tornado as a Kind of Jet-Effect

The inventor points out to the fact that a source of the natural tornadois two meeting relatively slow winds, resulting in that an arisen weakvortex is gradually transforming into a strong tornado. As well, theinventor takes note that the tornado brings rain, i.e. it condensesairborne vapors into water-aerosols and further into drops of rain. I.e.the tornado reduces the temperature down to the dew-point temperatureeven in a warm day. In other terms, the tornado, as an openthermodynamic system, decreases its entropy as well. This is anadditional example, wherein the temperature of air is transformed intothe kinetic energy of airflow. Hence, the natural tornadoself-acceleration is a kind of the jet-effect. In spite of the fact,that the efficiency of the tornado jet-effect is attractively high, thephenomenon remains unused in the world industry.

Further, the inventor points out that the well-known Great Red Spot ofJupiter is a stabilized tornado having portions of gas having the staticpressure of about 100 kPa and rotating with the velocity of about 180m/sec. Looking ahead, in view of the description referring to FIG. 9e ofthe invention, it will be evident to a person studied the invention,that an artificially or naturally created tornado becomes stabilizedwhen the effective velocity of a certain portion of rotating gas isreaching the specific M-velocity, depending on the effective adiabaticcompressibility parameter of the gas.

As well, the inventor points out that the well-known Saturn's Hexagon isa stabilized tornado having built-in stabilized specific spatialdistribution of velocities in the form of a regular hexagon. Lookingahead, in view of the description referring to FIG. 9e of the invention,it will be evident to a person studied the invention, that anartificially or naturally created tornado becomes stabilized andspecifically shaped when the effective velocity of a certain portion ofrotating gas is reaching the specific M-velocity, depending on theeffective adiabatic compressibility parameter of the gas. Further, theinventor points out that the stabilized cycling motion can betransformed into a stabilized oscillating motion generating peculiarwaves interfering constructively.

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system implementingthe tornado jet-effect providing the scalable and controllable use ofthe acquired power in the industry.

Betz s Law Applicability and Confusing-Paradoxical Approach

Betz's law, derived in frames of the continuum mechanics, is declared asapplicable to a hypothetical incompressible fluid stream undergoing anisothermal process and indicates the maximum power that can be extractedfrom wind, considered as such a fluid stream. The maximum power isindependent of the design of a wind turbine in open flow. The law isderived from the principles of conservation of mass and momentum of thefluid stream flowing through an idealized “actuator disk”, that can beimagined as effective cross-section covered by blades of the rotor, thatextracts kinetic-power from the wind stream. According to Betz's law, noturbine can capture more than 16/27 (59.3%) of the kinetic-power inwind. The factor 16/27 (0.593) is known as Betz's coefficient.

One explains the Betz approach as follows. Consider that if all of thekinetic energy coming from the wind moving through a turbine's effectivecross-section was extracted as useful energy the wind speed afterwardwould drop to zero. If the wind stopped moving at the exit of theturbine's effective cross-section, then no more fresh wind could getin—it would be blocked. In order to keep the wind moving through theturbine's effective cross-section, there has to be some wind movement,however small, on the other side with a wind speed greater than zero.Betz's law shows that as the fluid flows through a certain area, andwhen it slows from losing the kinetic energy to extraction from aturbine, it must spread out to a wider area. The mass conservation lawand the energy conservation law, both applied to the hypothetical caseof incompressible fluid stream undergoing an isothermal process, limitany turbine efficiency to 59.3%. The Betz limit has no dependence on thegeometry of the wind extraction system; therefore, the cross-sectionalarea of the rotor may take any form, providing that the flow travelsfrom the entrance to the exit and wherein the control volume has uniformentry and exit velocities. Any extraneous effects can only decrease theperformance of the system (usually a turbine) since this analysis wasidealized to disregard friction. Any non-ideal effects would detractfrom the energy available in the incoming fluid, lowering the overallefficiency.

To analyze an applicability of the Betz law in practice, reference isnow made to prior art FIG. 1k , a schematic illustration of a windturbine 17.1 built-in into cylinder 17.2 having real sidewalls and openbutt-ends. A constant cross-sectional area 17.3 is equal to theeffective cross-sectional area covered by rotor's blades and equals A₄₁.Cylinder 17.2 is exposed to ambient fluid stream, which, when yet to besubjected to the influence of cylinder 17.2 supplied by wind turbine17.1, has density ρ₄₀ and velocity u₄₀. When portion 17.40 of the fluidstream becomes subjected to a substantial influence of cylinder 17.2supplied by wind turbine 17.1, it is considered as composed ofsub-portions 17.41 and 17.42. Sub-portion 17.41 of the fluid streamenters cylinder 17.2 with a certain headway-motion velocity, indicatedby u₄₁. Sub-portion 17.42 of the ambient fluid stream has across-sectional area, indicated by A₄₂, equal to the difference betweencross-sectional area 17.6 and cross-sectional area 17.3, and flowsoutside cylinder 17.2 with headway-motion velocity, indicated by u₄₂. Asthe condition of mass conservation must be satisfied, thenρ₄₀(A₄₁+A₄₂)u₄₀=ρ₄₁A₄₁u₄₁+ρ₄₂A₄₂u₄₂, where ρ₄₁ and ρ₄₂ are densities ofsub-portions 17.41 and 17.42, correspondingly.

One expects that:

-   -   according to the mass conservation law, sub-portion 17.51 of the        fluid stream outflows from cylinder 17.2 with the headway-motion        velocity u₅₁, which is equal to the headway-motion velocity u₄₁        of entering sub-portion 17.41, while the fluid stream density        change is negligible;    -   blades of wind turbine 17.1, being subjected to the stream        action, are forcedly rotating and thereby generating an        electrical power; and moreover, outflowing sub-portion 17.51        gets also a certain rotational component of motion. I.e. the        resulting kinetic energy of the outflowing sub-portion 17.51        becomes increased with respect to the kinetic energy of entering        sub-portion 17.41, wherein, the kinetic energy increase is        defined by a value proportional to the second power of the        acquired rotational component of velocity.        This intuitive expectation is paradoxical from the point of view        of the Betz approach because one expects to harvest electrical        power and observe accelerated or at least not retarded        outflowing sub-portion 17.51 of the fluid stream simultaneously.

Some inventors have made claims of exceeding the Betz limit by usingnozzles. Some examiners interpret it as misrepresenting the Betz limitby calculating only the area, covered by the rotor blades, and not thetotal input of air contributing to the wind energy extracted from thesystem. In other words, the idealized “actuator disk” is interpreted aswider than the cross-section, covered by the rotor blades; and theelectrical power, produced by wind turbine 17.1, is harvested at theexpense of the kinetic-power of fluid stream portion 17.40 as a whole.

Again, referring to prior art FIG. 1k , consider a hypothetically idealwind turbine 17.1 exposed to an ambient fluid stream, having oncomingportion 17.40, wherein now, in general, cylinder 17.2 is either real orimaginary, i.e. sub-portions 17.41 and 17.51 may differ in velocity. Forsimplicity and without loss of reasoning, assume that outflowingsub-portion 17.51 does not get a rotational component of motion in theideal case. The kinetic-power of fluid stream portion 17.50 as a whole,which being subjected to the influence of wind turbine 17.1, equals(W ₅₁ +W ₅₂)=(½)×(ρ₅₁ A ₅₁ u ₅₁ ³+ρ₅₂ A ₅₂ u ₅₂ ³)where indexes “51” and “52” indicate sub-portions 17.51 and 17.52correspondingly, W₅₁ and W₅₂ are kinetic-powers, u₅₁ and u₅₂ areeffective velocities, ρ₅₅ and ρ₅₂ are effective densities, and A₅₁ andA₅₂ are cross-sectional areas. The kinetic-power of fluid stream portion17.40 as a whole, which being uniform and yet to be subjected to theinfluence of wind turbine 17.1, indicated by W₄₀, equalsW ₄₀=(½)×ρ₄₀(A ₅₁ +A ₅₂)u ₄₀ ³,wherein u₄₀ and ρ₄₀ are correspondingly velocity and density of portion17.40 as a whole. The velocity u₄₀ can be expressed via the effectivevelocities u₅₁ and u₅₂ in accordance with the mass conservation law as:

$u_{40} = {\frac{{\rho_{51}A_{51}u_{51}} + {\rho_{52}A_{52}u_{52}}}{\rho_{40}\left( {A_{51} + A_{52}} \right)}.}$Comparing the kinetic-power of fluid stream portion 17.50 as a whole,equal to (W₅₅+W₅₂), with the kinetic-power of fluid stream portion 17.40as a whole, equal to W₄₀, and, taking into account that the Betzapproach assumes a hypothetically incompressible fluid i.e. ρ₄₀=ρ₅₁=ρ₅₂,one can derive that the kinetic-power difference (W₅₁+W₅₂)−W₄₀ is alwaysa positive value. For instance, considering the case when the conditionA₅₁=A₅₂ is satisfied, the difference is expressed as(W ₅₁ +W ₅₂)−W ₄₀=(⅜)×ρ₄₀ A ₅₁(u ₅₁ +u ₅₂)(u ₅₁ −u ₅₂)².The positive value on the right side of the equation says that thekinetic-power of flow portion 17.50 subjected to the influence of windturbine 17.1 is increased with respect to the kinetic-power of flowportion 17.40 yet to be subjected to the influence of wind turbine 17.1.This result is confusing-paradoxical from the point of view of the Betzapproach, assuming that the electrical power produced by wind turbine17.1 is harvested from (i.e. by reducing) the kinetic-power of fluidstream portion 17.40 as a whole. Therefore, the Betz approach is notsuitable to describe this case as well. Thereby, the approach, based onthe interpretation of airflow or streaming water as a hypotheticallyincompressible fluid stream undergoing an isothermal process and whereinthe control volume has uniform entry and exit velocities to apply Betz'slaw, is not adequate sufficiently and sometimes loses a practical sense.

There is therefore a need in the art for a method to provide a properanalysis of an aerodynamic system comprising a wind turbine, therebyallowing for an optimal design of an apparatus for stream energy use.

Vortex Tube

Prior art FIG. 1l is a schematic illustration of a well-known “vortextube” also known as the Ranque-Hilsch vortex tube. It is a mechanicaldevice 190 that separates a compressed gas 19.0 into hot 19.1 and cold19.2 streams. It has no moving parts. Pressurized gas 19.0 is injectedtangentially into a swirl chamber 19.3 and accelerates to a high rate ofrotation. Due to a conical nozzle 19.4 at the end of the tube 19.5, onlythe outer shell of the rotated gas 316 is allowed to escape at thebutt-end outlet 19.7. As a result, this portion 19.1 of the gas is foundto have been heated. The remainder of gas 19.6, which performs an innervortex of reduced diameter within the outer vortex, is forced to exitthrough another outlet 19.8. As a result, this portion 19.2 of the gasis found to have been cooled. In an exemplary application, if theentering air is compressed to 6.9 bars at 21° C., the hot stream may beof 76° C. and the cool stream may be of −34° C. There are differentexplanations for the effect and there is a debate on which explanationis best or correct. However, the absence of a strong theory of thephenomenon makes it difficult to design an optimal shape of the vortextube to reach a substantially more effective use of the phenomenon.

There is, therefore, a need in the art for a method and apparatus toprovide a correct optimal design of the vortex-tube inner shape to reachthe most efficient cooling flows.

Phenomenon of Hydrophobicity and the Beverley Clock

Hydrophobicity is the physical property of a matter, frequently called ahydrophobic matter. The hydrophobic matter is composed of moleculeswhich are seemingly repelled from a mass of water; and vice-versa,molecules of water are seemingly repelled from a mass of the hydrophobicmatter. The reason for hydrophobic interaction is the large energy ofthe hydrogen bond [attraction] between water molecules, superior theenergy of the interaction between the water molecules and molecules ofthe hydrophobic matter. Strictly speaking, there is no repulsive forceinvolved; it is a lack of attraction between the inter-contacting waterand hydrophobic matter. (In contrast, molecules of a so-calledhydrophilic matter are attracted to water.)

If the hydrophobic matter and water, both are in the liquid state, theinter-repelling results in separating the hydrophobic matter and waterby a boundary. On the one hand, the boundary is a hydrophobic surfacerepelling the water, and, on the other hand, the boundary is a watersurface repelling the hydrophobic matter.

Reference is now made to FIG. 1m , a prior art schematic illustration ofconstruction 15.0 representing the core mechanism of the well-knownBeverley Clock, which being situated in a conditioned room and locatedwithin a closed “locker” and so, at the first glance, seeming as aclosed system from the point of view of thermodynamics, isseemingly-confusing running, in principle, non-stop since 1864, despitenever having been manually wound up. Construction 15.0 comprises tank15.1 filled with water 15.2 and liquid hydrophobic oil 15.3. Becauseconstruction 15.0 is in the gravitational field of Earth and the densityof liquid hydrophobic oil 15.3 is lower than the density of water 15.2,separating boundary 15.4 is horizontal and liquid hydrophobic oil 15.3is above the separating horizontal boundary 15.4. Sinker 15.5 isfloating nearby separating boundary 15.4 between hydrophobic oil 15.3and water 15.2. The inter-contacting water 15.2 and liquid hydrophobicoil 15.3 are inter-repelling, i.e. molecules of both: water 15.2 andliquid hydrophobic oil 15.3 become subjected to the repellent action ofseparating boundary 15.4. The action causes the molecules, adjacent toseparating boundary 15.4, to have a tendency to vector their velocities,resulting in an asymmetrisation of degrees of freedom of the moleculesBrownian motion that is observed as acceleration of the molecules in aprevalent direction: upwards for hydrophobic oil 15.3 and downwards forwater 15.2, thereby compressing distant layers of the liquids. In turn,when the degrees of freedom of the molecules Brownian motion aredestabilized and changed, other molecules, at the moment belonging tothe distant layers of the liquids, get a tendency to refill the freedniche of the degrees of freedom, i.e. the other molecules get anopposite asymmetrisation of their degrees of freedom. Thus, the Brownianmotion of molecules becomes partially transformed into a convectivemotion, i.e. the molecules convective motion occurs at the expense ofthe degrees of freedom of the Brownian motion, i.e. at the expense ofthe liquids warmth. Thereby, the originated convective motion, consumingcaloric from the liquids warmth, can be interpreted as a kind ofjet-effect. The convection (accompanied by cooling, and so by changes ofdensities of the water and oil, and by associated changes in theArchimedes forces) moves sinker 15.5. The upwards and downwards swingingmotion of sinker 15.5 wounds up the clock-mechanism 15.6, i.e. sets theBeverley clock going, while the consumed caloric is continuouslyrefilled from the ambient air warmth.

Analogously (but without the obligatory presence of gravitation in acertain direction and without a sinker), two inter-contactinginter-repelling fluids are used in a modern well-known Atmos clock,which does not need to be wound up manually as well. Namely, aconstruction of the Atmos clock core mechanism [not shown here] has ahermetic box comprising an easily-evaporating ethyl chloride, being inthe mixed aggregate state: saturated-gaseous and liquid. The Van derWaals attraction forces for the liquid aggregate state are stronger thanthe Van der Waals attraction forces between the liquid and saturatedgas. This provides that the saturated-gaseous and liquid aggregatestates of ethyl chloride play roles of the two inter-contactinginter-repelling fluids (the inter-repelling is due to a lack ofattraction). The inter-repelling destabilizes the mixed state resultingin convection motion, dominantly, of the saturated gas. The convectionmotion occurs at the expense of the ethyl chloride warmth that isobserved as self-cooling of the ethyl chloride. Again, the convectivemotion, consuming caloric from the fluids warmth, can be interpreted asa kind of jet-effect. The tendency to the convecting gas self-cooling isaccompanied by a tendency to the convecting gas self-compression,according to the van der Waals law about the gas state. While theconsumed caloric is continuously refilled from the ambient air warmth,the self-compression and decompression of gas set the Atmos clock going.

In view of the foregoing description of the Beverley Clock coremechanism (i.e. construction 15.0) referring to FIG. 1m , it will beevident to a person skilled in the art that the core mechanism comprisesall the inherent attributes of a so-called heat-engine, open from thethermodynamics point of view, namely:

-   -   the liquid hydrophobic oil and water (when considered as matters        exposed to ambient warmth either substantially-constant or        varying), both playing the role of an inherent absorber of        warmth from the ambient air;    -   the hydrophobic surface, repelling nearby molecules, i.e.        triggering the jet-effect, i.e. triggering the convection        motion, accompanied by cooling, and thereby, playing the role of        an inherent so-called “cold sink”;    -   the moving sinker playing the role of an inherent so-called        working body, wherein the sinker's motion is a result of the        convective motion, accompanied by cooling, by changes of        densities of water and oil, and by associated changes in the        Archimedes forces; and    -   in the final analysis, the clock-mechanism, playing the role of        an outer object consuming power to perform a useful work;        wherein the energy acquired by the sinker (as working body) is        further divided between the sinker swinging and the        clock-mechanism wounding up.

In view of the foregoing description of the Atmos Clock core mechanism,it will be evident to a person skilled in the art that theaforementioned hermetic box can be filled with any easily-evaporatingmatter being in the mixed aggregate state: liquid and gaseous. Inprinciple, water, when being in the mixed aggregate state: liquid andvapor, can play the role of such a matter capable of a self-cooling.Namely, a hermetic container, partially filled with liquid-water andpartially filled with a substantially dry gaseous air, both being underthe atmospheric pressure and having the same temperature, is anexemplary seemingly closed but in reality open system from the point ofview of the thermodynamics. In this case, water molecules, which arespontaneously broken away from the surface of the liquid-water, becomehydrophobic by definition [i.e., formally, attraction forces betweenunder-surface liquid-water molecules having collective hydrogen bondsare stronger than the attraction forces between the liquid-water and thevapor (i.e. the water molecules which are broken away)]. This results inthat, statistically, the spontaneously broken away water molecules donot return to the liquid-water while and until the humidity of thesubstantially dry air is lower than normal for the current temperatureand static pressure within the hermetic container. The self-evaporationprocess (i.e. the self-separation between the liquid-water and vapor) isaccompanied by a self-decrease in temperature (it is well-known that thewater evaporation is an endothermic process). The self-decrease intemperature is a symptom of an openness of the thermodynamic system,wherein the openness is provided at least by the presence of theinter-contacting inter-repellent fractions: the liquid-water and vapor.

In spite of the fact that the effect of convection motion, in the finalanalysis, occurring at the expense of ambient warmth, is used forautosetting the clock going, the effect remains unused in an enlargedscale in the world industry.

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of a system implementingthe kind of jet-effect providing the motion due to the hydrophobicityfor a scalable use in industry.

Diversity of Mechanisms of Fluid Repellence

-   -   Diamagnetism is the property of an object, which causes it to        create a magnetic field in opposition of an externally applied        magnetic field, thus causing a repulsive effect such that        diamagnetic materials are repelled by a permanent magnet.        Specifically, an external magnetic field alters the orbital        velocity of electrons around their nuclei, thus changing the        magnetic dipole moment in the direction opposing the external        field. Diamagnetic materials are materials with a magnetic        permeability μ being less than μ₀ (i.e. a relative permeability        μ/μ₀ being less than 1, or a susceptibility ξ=1−μ/μ₀ being        negative). Thus, an applied magnetic field creates an induced        magnetic field in the diamagnetic materials in the opposite        direction, causing repulsive force acting on molecules of the        diamagnetic material. Consequently, diamagnetism is a form of        magnetism that a substance exhibits only in the presence of an        externally applied magnetic field. In particular, liquid-water        is a diamagnetic material, and, correspondingly, a permanent        magnet is water-repellent. In other words, the permanent magnet        originates the phobic-repulsive van der Waals forces, and so, in        this sense, the permanent magnet is interpreted as hydrophobic.        The induced diamagnetism is generally a quite weak effect in        most materials (for instance, the susceptibility ξ=1−μ/μ₀ of        liquid-water is of about −7×10⁻⁷), although superconductors        exhibit a strong effect (with ξ=−1). From the energetic point of        view, a diamagnetic material (for instance, liquid-water), when        submerged in the magnetic field of the permanent magnet,        “mobilizes” the internal heat energy (i.e. the energy of        Brownian molecular motion) to induce the diamagnetic field        directed against the magnetic field. In other words, the        diamagnetic field energy is induced at the expense of the water        warmth. [For comparison, paramagnetic and ferromagnetic        materials are characterized by attraction to the permanent        magnet. A ferromagnetic material submerged in the magnetic field        of the permanent magnet “regularizes” domains thereby increasing        the magnetic field, again, at the expense of the ferromagnetic        material warmth, and, in the final analysis, at the expense of        the ambient warmth.]    -   Archimedes' principle states that the upward buoyant force that        is exerted on a body immersed in a fluid, whether fully or        partially submerged, is equal to the weight of the fluid portion        that the body displaces and acts in the upward direction at the        center of mass of the displaced fluid portion. A portion of the        fluid, identical to the displaced fluid portion, has a tendency        to occupy the origin space that yet to be occupied by the body.        In other words, the motions of the fluid molecules have a        tendency to be distributed as the Brownian motion distorted,        first, by the gravitational field, and second, by the immersed        body. The distorted Brownian distribution of molecular motions        is interpreted as distorted, and namely, reduced heat energy.        Again, from the energetic point of view, the buoyant action is        triggered by the gravitational field and occurs at the expense        of the internal heat energy of the fluid submerged in the        gravitational field. The fluid (for instance, water) repels the        body and the immersed body is interpreted as fluid-repellent in        this sense. In other words, the immersed body originates the        phobic-repulsive van der Waals forces, and so, the immersed body        is either hydrophobic, or oleophobic, or omniphobic.    -   Convective heat transfer, often referred to simply as        convection, is the transfer of heat from one place to another by        the movement of fluids. Convection is usually the dominant form        of heat transfer in liquids and gases. Although often discussed        as a distinct method of heat transfer, convective heat transfer        involves the combined processes of unknown conduction (heat        diffusion) and advection (heat transfer by bulk fluid flow). For        example, thermal expansion of fluids may force the convection.        In other cases, natural buoyancy forces alone are entirely        responsible for fluid motion when the fluid is heated, and this        process is called “natural convection”. An example is the draft        in a chimney or around any fire. In natural convection, an        increase in temperature produces a reduction in density, which        in turn causes fluid motion due to pressures and forces when        fluids of different densities are affected by gravity. For        example, when water is heated on a stove, hot water from the        bottom of the pan rises, displacing the colder denser liquid,        which falls. Thereby, a heating component submerged in water        repels adjacent fluid portions, i.e. the heating component        itself is interpreted as fluid-repellent: either hydrophobic, or        oleophobic, or omniphobic. In other words, the heating component        originates the phobic-repulsive van der Waals forces. Again, the        fluid repellency occurs at the expense of the heat energy,        which, first, is acquired by the adjacent fluid portion, and        then, become transformed into the kinetic energy of the        convective motion.        Thus, all the mentioned kinds of fluid repellence are        characterized by inserted spatial asymmetries of:    -   degrees of freedom of molecular motions, and    -   the phobic-repulsive van der Waals forces,        both causing a distortion of the Brownian distribution of the        fluid molecular motions, wherein the energy of the distorted        Brownian distribution is interpreted as composed of the reduced        actually-Brownian motion energy and energy of the fluid        molecular motion in a prevalent direction (for instance,        convective motion). In other words, the mentioned motion in the        prevalent direction occurs at the expense of the Brownian motion        energy (i.e. the heat energy) yet to be distorted.        Model Simplifications in the Continuum Mechanics

In order to describe both the Venturi effect and the de Laval effect,the flowing fluid is modeled in the classical fluid dynamics theory ashypothetically consisting of many small volume portions. This approachis described in book “The Feynman Lectures on Physics”, volume 2,chapter 40 “Flow of Dry Water” by Richard P. Feynman, Robert B.Leighton, and Matthew Sands, where the term “dry water” is applied tostress the model simplifications, namely:

-   -   first, the assumption that there are no viscous forces between        the fluid small volume portions;    -   second, the fluid small volume portions are connected spaces;    -   third, the fluid being studied is a continuum, i.e. it is        infinitely divisible and not composed of particles such as atoms        or molecules;    -   forth, the small volume portion boundaries are impermeable for        the fluid matter and impenetrable for temperature; and    -   fifth, the assumption that the static pressure, acting on the        small volume portions' boundaries and being the only reason of        mechanical forces, is an abstraction having no molecular nature,        and wherein the small portions' boundaries are hypothetically        inert to the fluid's inter-molecular forces, i.e. are not phobic        with repulsive forces and not sticking with attractive forces,        as soon as the problem is formulated in frames of the continuum        mechanics.        In other words, the simplifications are inherent assumptions in        the classical continuum mechanics theory, ignoring the molecular        structure of fluid and ignoring the static pressure as a        thermodynamic parameter interrelated with the fluid density and        temperature in accordance with the van der Waals law of the        fluid state. In this approach, the classical equations of fluid        motion are derived. In a particular case of hypothetically        inviscid flow, the classical equations of fluid motion, known        also as the Euler equations, are applied. For viscous flow, to        overcome said first simplification, the Navier-Stokes equations        are used. The Navier-Stokes equations are the Euler equations        modified by involving into the consideration the viscous forces        between the fluid small volume portions. Again, the viscous        forces are introduced irrelative to the viscosity effect        physical nature. In 2000, the problem of the Navier-Stokes        equation solution existence and smoothness became one of the        Millennium Goals formulated by the Clay Mathematics Institute.        It is noted in the “The Feynman Lectures on Physics”, volume 2,        chapter 40, cited above, that even in the simplest case of no        moving fluid, the equation of hydrostatics: −∇P−ρ∇ϕ=0, where ∇        is vector differential operator, P is the fluid static pressure,        ρ is the fluid density, and ϕ is the stand for the        potential-energy-per-unit-mass (for gravity, for instance, ϕ is        just gz, where g is the gravitational acceleration and z is the        height above the Earth's ocean surface level), in general, has        no solution, as soon as both: the pressure P and the density p        are spatially dependent and not interrelated in the mentioned        simplified approach of the continuum mechanics theory. To        facilitate a numerical analysis in practice and to overcome said        second simplification, the Navier-Stokes equation further        modifications (for example, the Spalart-Allmaras hypothetical        model of turbulences), assuming that the chosen fluid portions        could be dismembered into smaller connected spaces, are applied        to computational fluid dynamics. However, the third, fourth and        fifth simplifications remain inexact, making that the fluid        model loses physical sense for thermodynamic and kinetic theory        of matter and, as a result, the classical fluid model, on the        one hand, has not exact solutions for compressible fluids, and        on the other hand, leads to paradoxical solutions for        incompressible and inviscid fluids. For example, the d'Alembert        paradox, derived from the Euler equations, in particular, says        that a body, moving in an incompressible fluid, does not        experience a drag force as an impact effect. Describing this        paradox, for example, “Encyclopedia of Fluid Mechanics” by J. D.        Jacob, Department of Mechanical Engineering, University of        Kentucky, Lexington, Ky. 40506-0108, comments that “in the        18^(th) century, it was at odds with both observation and        intuition of flow about a body in motion”, and further defines        the term “drag” as primarily related to a viscosity phenomenon,        neglecting by the impact effect. The Navier-Stokes equation        having introduced viscous forces makes the d'Alembert paradox as        latent. To provide the principles of thermodynamics, one adds        equations of gas laws to the Euler system of equations and        further approximates the equations numerically.

There is, therefore, a need in the art for a method to provide a propermodel of fluid motion to exclude paradoxical results and the paradoxicalnonexistence of an exact solution relating thermodynamic parameters andvelocity of fluid-flow.

One usually explains the Venturi effect by Bernoulli's principle,applied to a hypothetical incompressible fluid streaming within a pipe,having free-slip inner walls. In this case, Bernoulli's principle can bewritten in the following form:

$\begin{matrix}{{{{\rho_{c}\frac{u_{c}^{2}}{2}} + P_{c} + G_{c}} = {P_{0} = {Const}}},} & {{Eq}.\mspace{14mu}\left( {1a} \right)}\end{matrix}$where, considering the fluid unit volume portion moving through acertain cross-section marked by index “c”, u_(c) is the fluid portionvelocity that is inversely-proportional to the fluid portion'sassociated cross-sectional area A_(c), P_(c) is the static pressure onthe fluid portion's boundaries, ρ_(c) is the fluid portion densityassumed to be identical for any cross-section, and G_(c) is the fluidunit volume portion potential energy stored in the gravitational fieldof the Earth. The potential energy G_(c) near the Earth ground can bewell-approximated by z_(c)ρ_(c)g, where z_(c) is the effective height ofthe fluid portion above the Earth's ocean surface level, g is the is thegravitational acceleration near the Earth's ocean surface level, and P₀is the stagnation pressure. P₀ is also called either the total pressureor the flow head, and it remains constant along the fluid motiondirection.

To describe the de Laval effect phenomenon, the Euler equations are usedas references to derive the differential equation:

$\begin{matrix}{{\frac{dA}{A} = {\left( {M^{2} - 1} \right)\frac{du}{u}}},} & {{Eq}.\mspace{14mu}\left( {1b} \right)}\end{matrix}$where A is the flow cross-section area, u is the flow velocitycorresponding to the cross-section area, and M is the flow M-velocity,i.e. the velocity measured in Mach numbers. As the speed of sound in afluid depends on the fluid temperature, so the value M is temperaturedependent. Equation (1b) says that if the flow is relatively slow (i.e.M<1), then the narrowing of the flow cross-section (i.e. negative dA)corresponds to acceleration of the flow (i.e. positive du); and if theflow is relatively fast (i.e. M>1), then the widening of the flowcross-section (i.e. positive dA) corresponds to acceleration of the flow(i.e. positive du). Computational fluid dynamics using the classicalEuler equations provide numerical solutions for spatial distributions ofthe fluid velocity, static pressure, and temperature within the de Lavalnozzle. The distributions are illustrated schematically in FIG. 1c . InFIG. 1c the fluid flow M-velocity 150 at the critical condition point180 is given by M=1. On the one hand, equation (1b) says that utilizinga pipe having no a divergent part, the flow cannot be accelerated up tovelocities higher than the velocity of sound, i.e. up to M>1. On theother hand, equation (1b) allows for the acceleration of the fluid flowin a converging nozzle up to the velocity of sound, i.e. M≤1.

In practice, firstly, the de Laval effect occurs on M-velocitiessubstantially lower than M=1; and secondly, utilizing a pipe having no adivergent part, airflow cannot be accelerated up to velocities higherthan approximately only half of the velocity of sound in the air. Thus,the two mentioned equations (1a) and (1b), derived from the mentionedapproach, which assumes that the fluid consists of many small volumeportions having neither permeable boundaries nor molecular structure,have certain restrictions of applicability.

To design a shape of a convergent-divergent jet-nozzle one applies thefollowing equation:

$\begin{matrix}{{\frac{A}{A_{*}} = \left\lbrack \frac{1 + {\frac{j - 1}{2}M^{2}}}{1 + \frac{j - 1}{2}} \right\rbrack^{\frac{j + 1}{2{({j - 1})}}}},} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$derived basing on equation (1b), where A* is the minimal cross-sectionalarea at the critical condition point 180, and j is the gas adiabaticcompressibility-constant.

To design a rocket jet-nozzle for fluid portion acceleration from slowspeeds to high-subsonic speeds, and even up to speeds higher than thespeed of sound, some designers use modern software for computationalfluid dynamics analysis where the two equations: (1a) for the slow flowand (1b) for the fast flow, are programmed accordingly. The fact, thatthe two equations have restrictions of applicability at least becausethe equations allow for different ranges of the flow velocity, makes theanalysis inappropriate to simulate the expected jet-effect properly. Asa result, sometimes users are not satisfied by calculated solutionsbecause the algorithm “may experience robustness problems for slightlycompressible fluids”, as commented in the software help document:“CFX_PRE” Release 14.5-214 of ANSYS, Inc. and its subsidiaries andaffiliates, Page 215, Lines 6-7.

Moreover, for a case of “slightly compressible” slow-flowing gas, thesoftware help document recommends using “the Incompressible option”(“CFX_PRE”, Page 215, Line 7). However, a use of the Incompressibleoption for a slow-flowing gas, for which the static pressurere-distribution is allowed, is paradoxical, because an adiabatic processis described by the equation Pv^(j)=Const, where P is the gas portion'sstatic pressure, v is the gas portion volume, and j is the gas adiabaticcompressibility-constant, and so a relative change of the gas portionvolume is of the same order of value as a relative change of the staticpressure, namely,

$\frac{dv}{v} = {{- \frac{1}{j}}{\frac{dP}{P}.}}$

There is, therefore, a need in the art for a method and apparatus toprovide a proper analysis and optimal design of the convergent-divergentjet-nozzle shape to reach the most efficient jet-effect.

Furthermore, to formalize the viscous forces influence, theNavier-Stokes equation of fluid motion is expressed via a tensor ofviscosity coefficients characterizing the fluid. This formalization offluid flowing around a body using such a tensor of viscositycoefficients is not completely adequate at least because:

-   -   the viscous forces influence is dependent on material of the        body submerged in the flowing fluid (for instance, a hydrophobic        or hydrophilic body submerged in moving water); and    -   the viscosity coefficients should be functions of the spatially        distributed temperature of flow as the flow temperature is        interrelated with the spatially distributed static pressure of        flow, which, in turn, is interrelated with the spatially        distributed velocity of flow.

There is, therefore, a need in the art for a proper equation of fluidmotion, generalized in the frames of the kinetic theory of matter,taking into account kinds of the jet-effect (for instance, theCoanda-jet-effect and the phenomenon of hydrophobicity), and soadequately applicable to any flowing fluid and any material of a bodysubmerged in the flowing fluid, for instance, to moving water flowingaround a hydrophobic body.

Wave Equation in Frames of the Continuum Mechanics

The wave equation is an important second-order linear partialdifferential equation for the description of waves—as they occur inphysics—such as sound waves, light waves and water waves. It arises infields like acoustics, electromagnetics, and fluid dynamics. In 1746,d'Alembert discovered the one-dimensional wave equation, and within tenyears Euler discovered the three-dimensional wave equation.

The wave equation is a hyperbolic partial differential equation. Ittypically concerns a time variable t, one or more spatial variables x₁,x₂, . . . , x_(n), and a scalar function x=x(x₁, x₂, . . . , x_(n), t),whose values could model, for example, the mechanical displacement of awave. The wave equation for x is:

$\begin{matrix}{{\frac{\partial^{2}x}{\partial t^{2}} = {c^{2}{\nabla^{2}x}}},} & {{Eq}.\mspace{14mu}\left( {2a} \right)}\end{matrix}$where ∇² is the spatial Laplacian and c is a fixed constant.Solutions of this equation describe the propagation of disturbances outfrom the region at a fixed speed in one or in all spatial directions, asdo physical waves from a plane or localized sources; the constant c isidentified with the propagation speed of the wave. This equation islinear. Therefore, the sum of any two solutions is again a solution: inphysics, this property is called the superposition principle.

The principle of superposition is one of the most general laws in manysections of physics. In the simplest formulation, the principle ofsuperposition is:

-   -   The effect of a few external forces on a particle is the vector        sum of the effects of these forces; and    -   Any complex motion can be divided into two or more simple ones.

The wave equation alone does not specify a physical solution; a uniquesolution is usually obtained by setting a problem with furtherconditions, such as initial conditions, which prescribe the amplitudeand phase of the wave. Another important class of problems occurs inenclosed spaces specified by boundary conditions, for which thesolutions represent standing waves, or harmonics, analogous to theharmonics of musical instruments.

The elastic wave equation in three dimensions describes the propagationof waves in a stationary isotropic homogeneous elastic medium, whereinin the case of an electromagnetic field, the medium is a portion of theuniverse characterized by the universe background matter and theuniverse background energy. While linear, this equation has a morecomplex form than the equations given above, as it must account for bothlongitudinal and transverse motion:ρ{umlaut over (x)}=f+(λ+2μ)∇(∇·x)−μ∇×(∇×x)  Eq. (2b),where:

-   -   λ and μ are the so-called Lame parameters describing the elastic        properties of the medium, where μ is the shear viscosity        coefficient and λ is the dilatational viscosity coefficient;    -   ρ is the density,    -   f is the source function (driving force), and    -   x is the displacement vector with respect to the stationary        medium.

Note that in this equation, the force and the displacement, both arevector quantities. Thus, this equation is sometimes known as the vectorwave equation.

Taking note that the wave equation formulation remains in frames of thecontinuum mechanics, the medium characteristics defining the wave,namely, the velocity of sound, the density, and the coefficients Lame,the all are as kinds of normalizing constants only, and so do notprovide a description of an energetic interaction between the wave andmedium. This, in particular, is a reason of at least the followingconfusing paradoxes:

-   -   considering a wave as a process transmitting energy from a        wave-source to a point of observation with the velocity of        sound, a map of superposed two waves has points of destructive        and constructive interference, wherein an observer confusingly        discloses that the seemingly energy local annihilation occurs in        the destructive interference points and the seemingly energy        local excess arises in the constructive interference point, i.e.        the wave energy as though is not constant more and a seemingly        “tunnel effect”, that brings to mind something that defined in        the quantum mechanics, takes place;    -   if to implement a superposition of two identical but anti-phase        waves along a wave-guide, a complete-like annihilation becomes        expected;    -   if to implement a superposition of two (or several) identical        in-phase waves along a wave-guide, an excessive-like cumulative        power becomes expected, because the wave power is proportional        to the second power of the wave amplitude, so N in-phase        superposed amplitudes correspond to the cumulative power        increase by the factor N² (as, for instance, shown in book “The        Feynman Lectures on Physics”, volume 1, chapter 30 “Diffraction”        by Richard P. Feynman, Robert B. Leighton, and Matthew Sands),        moreover,    -   the wave equation (2a) and/or (2b), when assuming, on the one        hand, variations of displacement and, on the one hand, a        constant density of the medium, inevitably runs on a violation        of the law of continuity;    -   it is assumed that, for fluids, the shear viscosity coefficient        Lame u equals zero, however, as the wave processing in the        fluids assumes local accelerating motions of the fluid portions,        which [the accelerating motion] is inevitably interrelating with        varying of the fluid portions cross-sectional area, in addition,        the phenomenon of an adiabatic convective self-acceleration due        to the Coanda-jet-effect is inevitable as well, as described        hereinbefore referring to FIGS. 1b and 1f , in turn, the        inevitably varying cross-sectional area is interpreted as an        inherent local shear motion, hence, in order to formalize the        inherent shear motion in frames of the continuum mechanics, one        must use the non-zero shear viscosity coefficient Lame u; and    -   in a well-known so-called “thermo-acoustic heat engine”, an        acoustic resonator plays the role of a “cold sink” that doesn't        follow from the wave equations (2a) and (2b).

Moreover, the legendary story about mystery experiments with Tesla'smechanical oscillator claimed as Tesla's earthquake machine, if notexplained especially, remain unbelievable.

There is, therefore, a need in the art for a proper approach to the waveequation, generalized in the frames of the kinetic theory of matter, andthereby providing for the physical sense; as well, there is, therefore,a need in the art for a proper analysis of resonating waves to providefor efficient and controllable practical use of elastic wavesconstructive interference in industry.

In relation to electromagnetic oscillators, Tesla coils are unique inthe fact that they create extremely powerful electrical fields. Aseemingly significant power disbalance between input and output in thefamous experiments with Tesla coil, if not explained especially, remainsconfusingly-paradoxical. Today, the main use of the Tesla coil is forentertainment and educational displays, and small coils are still usedtoday as leak detectors for high vacuum systems only.

There is, therefore, a need in the art for a proper understanding ofresonating waves to provide for efficient and controllable practical useof constructive interference of electromagnetic waves and/or electricsignals in industry.

Radiation Pressure

In electrodynamics, radiation pressure is the pressure exerted upon anysurface exposed to electromagnetic radiation. The radiation pressureimplies an interaction between electromagnetic radiation and bodies ofvarious types, including clouds of particles or gases. Theelectromagnetic radiation pressure is determined in Maxwell's theory bythe so-called Poynting vector or, strictly speaking, the time-averagedPoynting vector. Considering an electromagnetic wave, the Poyntingvector is proportional to the vector multiplication of the electricalfield by the magnetic field of the electromagnetic wave, so thetime-averaged Poynting vector is oriented to the direction ofelectromagnetic wave propagation and the magnitude of the time-averagedPoynting vector is proportional to the time-averaged intensity of theelectromagnetic wave. The forces generated by the radiation pressure aregenerally too small to be detected under everyday circumstances;however, they do play a crucial role in some settings, such as astronomyand astrodynamics; furthermore, for example, a so-called solar sail ofspacecraft is based on the effects of the Sun's radiation pressure.

In acoustics, acoustic radiation pressure, called also sound radiationpressure, or, briefly, sound pressure, is the time-average excesspressure on an obstacle exposed to the sound. The acoustic radiationpressure is determined by the pulse wave transmitted per unit time perunit area of obstruction and determined by the so-called Umov-Poyntingvector, as the Poynting vector, but generalized for the case of acousticwaves propagating in a homogeneous elastic fluid medium. A redirectionof the Umov-Poynting vector results in the acoustic radiation pressure,in particular:

-   -   The acoustic radiation pressure generated by the acoustic beam:        -   having a confined front area of a plane wave,        -   propagating in an infinite undisturbed environment, and        -   being incident on a fully reflecting flat surface at the            right angle,    -   (i.e. when the Umov-Poynting vector is subjected to redirection        on 180°)    -   is called Langevin radiation pressure; and    -   At normal incidence on a flat surface fully reflecting a portion        of an omnidirectional sound (i.e. when the Umov-Poynting vector        is subjected to omnidirectional scattering, caused by        non-linearity of the medium, resulting in the effective        redirection of the scattered Umov-Poynting vector on 180°), the        acoustic radiation pressure is called Rayleigh radiation        pressure.

The pressure of sound radiation is the effect of the second order; so,in zero gravity, one can design an acoustic pusher for stabilizingobjects in indoor space and for pumping of fluids.

Bernoulli Theorem

In contrast to a popular description of Bernoulli's principle as asimplification of the Euler equation of momentum conservation originallyallowed for an inviscid flow and further applied to anexclusively-incompressible fluid, as made, for example, in the“Encyclopedia of Fluid Mechanics” by J. D. Jacob cited above, “TheFeynman Lectures on Physics”, volume 2, chapter 40, also cited above,demonstrates the Bernoulli theorem proof basing on general assumptionsthereby showing the Bernoulli theorem widened sense.

For the purposes of the present patent application, in contrast to theterm “Bernoulli's principle”, applied to describe a hypotheticalparticular case of the Euler equations, the term “Bernoulli theorem” isapplied to the proven interrelation of flow characteristics.

Prior art FIG. 2 is a schematic illustration of stationary fluid flowstreamlines 20 forming walls 24 of an imaginary pipe. Consider afragment 23 of the imaginary pipe that has open ends: inlet 21 andoutlet 22. The imaginary pipe walls 24 by definition are impermeable, assoon as they are formed by streamlines 20; and the shape of walls 24 isnot restricted regarding constriction or stretching. The fluid may becompressible-expandable and viscous as a real fluid; and, one assumesfor simplicity that the fluid matter is subjected to neither chemicalreactions nor phase changes within the pipe fragment 23. Inlet 21 areais A₁, where the fluid has inner-static-pressure P₁, density ρ₁, andvelocity u₁. The area of outlet 22 is A₂, where the fluid hasinner-static-pressure P₂, density ρ₂, and velocity u₂. After ashort-time interval T, a portion of the fluid entering inlet 21 has massm₁ calculated as m₁=ρ₁A₁u₁τ. A mass m₂ leaves the pipe fragment 23through outlet 22, i.e. m₂=ρ₂A₂u₂τ.

The law of flow mass conservation requires that m₁=m₂=m, thereby,m=ρ ₁ A ₁ u ₁τ=ρ₂ A ₂ u ₂τ  Eq. (3a).The equation of continuity, namely: ρ₁A₁u₁=ρ₂A₂u₂, follows from (3a).

Note that the entering mass has the gravitational potential energy, thatnear the ground of the Earth can be well-approximated by G₁=z₁ mg; whilethis mass leaving the pipe fragment 23 has the gravitational potentialenergy G₂=z₂ mg, where z₁ and z₂ are correspondingly inlet 21 and outlet22 cross-sections' effective heights above the Earth's ocean surfacelevel.

On the other hand, one can calculate work, done by the fluid flow staticpressure. The work at inlet 21 equals dW₁=P₁A₁u₁τ, meaning that the flowmass acquires the energy portion dW₁; and the work at outlet 22 equalsdW₂=P₂A₂u₂τ, meaning that the flow mass losses the energy portion dW₂.

Add the work dW₁ to the potential and kinetic energies of the massportion at inlet 21 in order to define the total energy of the enteredmass portion, namely:

$U_{1} = {{{dW}_{1} + G_{1} + \frac{{mu}_{1}^{2}}{2}} = {{P_{1}A_{1}u_{1}\tau} + {z_{1}m\;{\mathcal{g}}} + \frac{{mu}_{1}^{2}}{2}}}$Analogously, add the work dW₂ to the potential and kinetic energies ofthe mass portion at outlet 22 in order to define the total energy of themass leaving portion, namely:

$U_{2} = {{{dW}_{2} + G_{2} + \frac{{mu}_{2}^{2}}{2}} = {{P_{2}A_{2}u_{2}\tau} + {z_{2}m\;{\mathcal{g}}} + \frac{{mu}_{2}^{2}}{2}}}$

Considering an adiabatic process, i.e. conservation of the total energyin the pipe fragment 23, one applies the energy conservation lawrequiring that the entering energy U₁ must be equal to the leavingenergy U₂, i.e.

$\begin{matrix}{{{P_{1}A_{1}u_{1}\tau} + {z_{1}m\;{\mathcal{g}}} + \frac{{mu}_{1}^{2}}{2}} = {{P_{2}A_{2}u_{2}\tau} + {z_{2}m\;{\mathcal{g}}} + \frac{{mu}_{2}^{2}}{2}}} & {{Eq}.\mspace{14mu}\left( {3b} \right)}\end{matrix}$Dividing the components of the equation (3b) on the value of mass mdefined in equation (3a), one obtains the following equation:

$\begin{matrix}{{{\frac{P_{1}}{\rho_{1}} + {z_{1}{\mathcal{g}}} + \frac{u_{1}^{2}}{2}} = {\frac{P_{2}}{\rho_{2}} + {z_{2}{\mathcal{g}}} + \frac{u_{2}^{2}}{2}}},} & {{Eq}.\mspace{14mu}\left( {3c} \right)}\end{matrix}$from which the well-known Bernoulli theorem formulation follows, namely:the value P_(i)/ρ_(i)+z_(i)g+u_(i) ²/2 is constant along any streamlineof a fluid flow, i.e.

$\begin{matrix}{{\frac{P_{i}}{\rho_{i}} + {z_{i}{\mathcal{g}}} + \frac{u_{i}^{2}}{2}} = {Const}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$

The constant Const on the right side of equation (3) performs the totalenergy of the fluid portion unit mass moving along a streamline, whereinthe items: P_(i)/ρ_(i), z_(i)g, and u²/2 define kinds ofenergy-per-unit-mass of the fluid portion, namely: P_(i)/ρ_(i)interrelates with the internal heat energy stored in molecular Brownianrandom motion and interactions, wherein, according to the kinetic theoryof ideal gas, the ratio P_(i)/ρ_(i) is defined as proportional to thegas temperature, z_(i)g defines the potential-energy-per-unit-massstored in the Earth's gravitational field, and u²/2 defines thekinetic-energy-per-unit-mass. In hydrodynamics, one normally assumesthat the liquid density ρ is not varying. In this hypotheticalparticular case, equation (3) can be rewritten in terms of pressure as:P_(i)+ρz_(i)g+ρu_(i) ²/2=P₀, where P₀ is the total pressure or the flowhead being constant along any streamline of the incompressible liquid,ρu_(i) ²/2 is the partial dynamic pressure, P_(i) is the partialinner-static-pressure provided by the fluids molecules [note that theclassical continuum mechanics theory, and in particular, thehydrodynamics does not refer to a molecular structure of matter], andρz_(i)g is the partial potential-static-pressure provided by the Earth'sgravitational field.

Considering the ratio P_(i)/ρ_(i) as a measure of fluid's internalenergy, the Bernoulli theorem proof is based on the laws of the energyconservation and matter continuity and has not especial demands onviscosity and compressibility-expandability of the considered fluid. TheBernoulli theorem proof is general and does not conflict with thethermodynamic and kinetic theory of fluid. Thus, the Bernoulli theorem,as a form of the energy conservation law, is applicable for any fluidthat may be compressible-expandable and viscous as a real fluid. Animportant feature of the proof is the assumption that imaginary fragment23 is a flow portion, but not a real pipe.

Prior art FIG. 3 shows a fragment of pipe 33, having real walls 34. Whenone ignores turbulences caused by walls 34 and the heat exchange betweenthe walls and fluid, without loss of generality, fragment 23 of theimaginary pipe (FIG. 2) is built-in into real pipe 33. Nonetheless, realwalls 34 being sticking for the fluid's molecules, causing, in general,an origination of turbulence and the heat exchange between the walls andfluid, such that the energy conservation, written as equation (3),becomes not perfectly exact; the Bernoulli theorem may play a role of acriterion of adequacy for the equation of fluid motion applied, inparticular, to convergent-divergent jet-nozzle design and analysis aswell as for a computational fluid dynamics numerical solution.

Equation (1a) is a particular case of the Bernoulli theorem applied to ahypothetical incompressible fluid flow. Also, only the particular caseof the Bernoulli theorem applied to a hypothetical incompressible fluidflow can be derived from the Euler equations. In fact, the mentionedsimplifications of continuum mechanics render the Euler andNavier-Stokes equations as having no exact solutions; and the Euler andNavier-Stokes equations numerical approximation, in the general case,conflicts with the Bernoulli theorem. Thus, the Euler and Navier-Stokesequations may be applicable to an ideal case, for which the effects ofmolecular interactions, at least such as diffusion and/or heat exchangebetween the fluid portions and/or the viscous fluid motion inherentlyaccompanied by the diffusion, are negligible.

For the purposes of the present patent application, the term “Bernoullitheorem” is applied as more correct, to stress the proven interrelationexpressed as equation (3), than the term “Bernoulli's principle”,assuming a hypothetical particular case of the Euler equations andexpressed in the form of approximated equation (1a).

There is, therefore, a need in the art for a method and apparatus,corresponding to strongly proved criteria, applicable to slow as well asto fast flowing real compressible-expandable fluids, and providing acorrect optimal design of the convergent-divergent jet-nozzle in orderto reach the most efficient jet-effect.

SUMMARY OF THE INVENTION

Unity and Novelty of the Invention

Generally, the unity and novelty of the invention are in a methodproviding for a specific actually-airfoil shaping and covering of a bodysubmerged in a forcedly or naturally moving fluid, wherein the specificshaping and covering allows to harvest a useful-beneficial power fromthe ambient medium heat using an enhanced jet-effect, in particular, theCoanda-jet-effect reinforced repeatedly and the waving jet-effectreinforced by constructive interference, wherein the logic to reinforcewave power of elastic waves is spread also to electromagnetic waves.

More particularly, the unity and novelty of the invention provide forthe following.

The methodological unity of the present invention is in use of a novelmethod for computational fluid dynamics applied to a flowing fluid,composed of moving and interacting molecules, wherein, in contrast tothe continuum mechanics approach, the fluid static pressure,temperature, density, and flow velocity are defined in terms of thekinetic theory of matter. The method provides for a numerical estimationof spatially distributed parameters: the three components of thevelocity-vector, the temperature, the density, and the static pressureof the moving fluid; wherein, taking into the consideration a molecularstructure of the fluid matter, the method allows for a designing ofelaborated airfoil and, in particular, hydrophobic corpuses and corpusescomprising specifically shaped actually-airfoil tunnels.

The phenomenological unity and novelty of the present invention is in ause of an enhanced jet-effect that is specified as an efficienttransformation of the fluid internal heat energy, performed as kineticenergy of the molecules Brownian random motion, into the fluid jetstreamkinetic energy, performed as kinetic energy of the molecules motion in aprevalent direction. The transformation is caused by theCoanda-jet-effect operation. In particular, when the molecules motion inthe prevalent direction is an oscillating motion, the Coanda-jet-effectoperation performs the waving jet-effect resulting in elastic wavespropagation.

The implementation unity of the present invention is in the novelspecific actually-airfoil shaping of bodies submerged in the flowingfluid. Wherein, on the one hand, the mentioned properties of fluidmatter contacting with the bodies' surfaces, and, on the other hand, thebodies' specific actually-airfoil shapes defined and calculatedaccording to the novel method, altogether are resulting in an enhancedjet-effect, observed as an effect of increased acceleration of a fluidportion at the expense of the fluid matter warmth. Namely, the specificactually-airfoil shaping is such that the bodies' surfaces act on theflowing fluid portion according to the Coanda-jet-effect operationcausing transformation of the fluid portion's internal heat energy intothe fluid portion's additional acquired kinetic energy. In other words,the Coanda-effect operation transforms a part of the kinetic energy ofthe fluid molecules Brownian random motion [i.e. the heat energy], intothe kinetic energy of the molecules motion in a prevalent direction[i.e. into either the acquired kinetic energy of a jetstream and/or theacquired wave power of an acoustic wave]. In a more general case, whenthe fluid flow is turbulent, comprising whirling groups of molecules,the Coanda-effect operation results in partial aligning also of theturbulent motion of the whirling groups of molecules with the body'ssurfaces, that is observed as an increase of the effective velocity ofthe flow portion, accompanied by the portion's inner turbulencedecrease, as the fluid portion passes nearby the body. Thus, thisresults in an increase of the fluid portion's kinetic energy also at theexpense of the fluid portion's inner turbulent energy.

-   -   In a case, wherein the fluid is water and the body's surface is        hydrophobic, the water portions are subjected to an acceleration        that can be utilized at least to reduce a skin-friction        resistance to provide a free-slip condition of motion;    -   in a case, wherein the fluid is a substantially        compressible-expandable gas, such as air at high velocities, the        specific shaping results in a convergent-divergent flowing,        accompanied by an enhanced jet-effect, that can be utilized at        least for an efficient harvesting of electricity using either a        wind turbine, capable to transform mechanical motion of flow        into electricity, and/or a Peltier element, capable to operate        as a thermoelectric generator producing electricity from the        temperature difference caused by the jet-effect; and    -   in a case, wherein the originated motion of fluid is an        oscillating motion inherently accompanied by propagating waves        accompanied by the waving jet-effect, the waving jet-effect        reinforced repeatedly by constructive interference of the waves        can be utilized at least for an efficient harvesting of        electricity using a detector of waves as a power converter;        wherein the logic is spread also to electromagnetic waves.        Primary Basic Features of the Present Invention

One of the primary features of the present invention is that, incontrast to the classical approach of continuum mechanics, the terms“fluid”, “flow velocity”, “temperature”, “static pressure”, and“density” are defined taking into the consideration a molecularstructure of a substance according to the kinetic theory of matter.Namely, the term “fluid” is defined as a substance composed of movingand interacting molecules, the term “flow velocity” relates to aprevalent motion of molecules, the term “temperature” is defined by themolecules random motion as a measure proportional to the averagemolecular kinetic energy of the molecules Brownian random motion, theterm “static pressure” is defined as a measure of the randomly movingmolecules cumulative impact, and the term “density” is defined as ameasure of the molecules concentration and mass, equal to said molecularfluid mass per unit volume.

Another primary feature of the present invention is that the specificM-velocity is defined as a characteristic of the molecular compositionof the fluid.

Yet other one primary feature of the present invention is that anapparatus, shaped specifically, is defined as inherently submerged in aflowing fluid, having at least a specific so-called adiabaticcompressibility parameter, and the definition of the specificactually-airfoil shape of the apparatus's corpus is accompanied by thedefinition of the specific properties of the molecular fluid,altogether, allowing for an optimized implementation, in general, of theCoanda-effect, and, in particular, of the de Laval effect. Wherein thede Laval effect should be understood in a widened sense as comprisingboth: the de Laval jet-effect, defined as an effect of flowextra-acceleration, and the de Laval retarding-effect, defined as aneffect of flow extra-slowing.

A further feature of the present invention is that, in contrast to theclassical approach of continuum mechanics, the terms “drag”,“skin-fiction”, “osmotic-like effect”, and “viscosity” are defined,referring to the kinetic theory of matter. Namely:

-   -   the drag is an effect of asymmetrical, disbalanced impact of        molecules, observed when a shape of a fluid portion, flowing        around a body corpus, is subjected to a deformation, such that        the drag-effect is defined as a cumulative effect comprising        stagnation-effects and the Coanda-effect;    -   the skin-friction is an effect of fluid molecules sticking to a        nearby wall, resulting in a specific spatial distribution of        moving-small-portions velocities, when the moving-small-portions        flow in a boundary layer adjacent to the nearby wall;    -   the osmotic-like effect is defined as an effect of exchange of        molecular matter and heat between moving-small-portions; and    -   the effect of viscosity is defined as a cumulative effect        comprising the skin-friction effect and the osmotic-like effect;

An additional feature of the present invention is that, in contrast tothe classical approach of electrodynamics, the term “vacuum” isredefined as “filled” by the universe background matter and by theuniverse background energy, comprising at least:

-   -   the energy of gravitational field,    -   the so-called dark energy,    -   the internal heat energy stored in the neutrino gas interpreted        in terms of the kinetic theory of matter, and    -   the latent electromagnetic energy, hidden by the so-called        destructive interference, to which the background        electromagnetic radiation is subjected,        in accordance with the modern consensus of scientists.        Principal Objects

Accordingly, it is a principal object of the present invention:

-   -   to overcome the limitations of existing methods and apparatuses:        -   for designing actually-airfoil profiles of birdlike wings;        -   for designing actually-airfoil convergent-divergent            jet-nozzles, providing the enhanced jet-effect;        -   for designing in-line arranged sequences of elemental            jet-boosters, providing the Coanda-jet-effect reinforced            repeatedly and thereby resulting in jet-thrust reinforced            repeatedly, correspondingly; and        -   for designing in-line arranged sequences of elemental            jet-boosters, destined for triggering the waving jet-effect            reinforced repeatedly by constructive interference of forced            in-phase acoustic waves; and    -   to provide improved methods and apparatus for efficient use of        the desired jet-effect, namely, the Coanda-jet-effect, and/or        the de Laval jet-effect, and/or the waving jet-effect for        either:        -   increasing efficiency of vehicle jet-engines, and/or        -   harvesting electrical energy from fluid warmth, and/or        -   increasing efficiency of cooling flows, and/or        -   water harvesting from air.            It is an object of the present invention to provide methods            and apparatus for:    -   an enhanced jet-effect implementation at high-subsonic        velocities avoiding the unwanted phenomenon of the Mach waves        emission;    -   jet-effect use at high-subsonic velocities avoiding the        phenomenon of shock sound-wave emission;    -   jet-effect use in jet-boosters and rocket nozzles at        low-subsonic, high-subsonic, transonic, supersonic, and        hypersonic velocities;    -   design of an actually-airfoil wing, improved by jet-effect        efficiency;    -   design of a vortex tube, improved by cooling efficiency;    -   design of actually-airfoil convergent-divergent jet-nozzles        providing for a jet-effect applied to electricity producing from        a fluid warmth using classic at least one of a wind-turbine, a        hydro-generator, a turbo-generator, and a Peltier element [i.e.        a thermoelectric generator] as well as using a modified improved        wind-turbine, constructed according to the principles of the        present invention to operate under a fast airflow;    -   design of hydrophobic jet-gears applied to electricity producing        from water warmth using at least one of a hydro-generator and a        Peltier element;    -   design of convergent-divergent jet-nozzles applied to water        harvesting from air;    -   design of a vehicle jet-engine, having an improved        net-efficiency;    -   more reliable design of elaborated actually-airfoil bodies;    -   multi-stage cascading the Coanda-jet-effect operation by        sequential cascading of airfoil bodies; and    -   multi-stage enforcing the waving jet-effect operation by        implementing constructive interference of waves, either elastic        and/or electromagnetic.

In one exemplary embodiment, a method is disclosed for computationalfluid dynamics; wherein the method is based on generalized equations offluid motion derived from conservation laws, and laws of thermodynamicsand the kinetic theory of matter. The generalized equations of fluidmotion have an exact solution, the adequacy of which is confirmed byboth: the Bernoulli theorem and the van der Waals law of gas state. Themethod is proper for numerical simulations:

-   -   of fluid headway flows at low-subsonic, high-subsonic,        transonic, supersonic, and hypersonic velocities, as well as    -   of fluid oscillations accompanied by acoustic waves,        and applicable to almost incompressible fluids as real liquids        as well as to compressible-expandable fluids as real gases.

In another exemplary embodiment, a fluid-repellent jet-gear submerged ina fluid is disclosed. The fluid-repellent jet-gear has an asymmetricallyshaped corpus comprising an outer layer contacting with the fluid,wherein the outer layer is made from a fluid-repellent material,triggering a phobic-repulsing jet-effect, thereby enabling motion at theexpense of the internal heat energy of the fluid.

In one further exemplary embodiment, a convergent-divergent jet-nozzleis disclosed. The convergent-divergent jet-nozzle has a specificallyshaped inner tunnel, providing linearly increasing the gas M-velocityalong the line of gas motion; wherein the improved linearity at least inan essential M-velocity range comprising the specific M-velocity is acriterion of the convergent-divergent jet-nozzle tunnel shapeoptimization according to an exemplary embodiment of the presentinvention.

In yet one exemplary embodiment, a two-humped airfoil wing design isdisclosed. The two-humped airfoil wing provides increased lift-effect athigh-subsonic transonic, supersonic, and hypersonic velocities.

In one other exemplary embodiment, a flying capsule is disclosed, havinga specifically shaped inner tunnel and airfoil outer profile; whereinwhen fast-flying, the variable cross-sectional area of the tunnelresults in an enhanced jet-effect.

In still another exemplary embodiment, an aggregation ofcircumferentially arranged elemental jet-boosters is disclosed,representing a vortex generator providing acceleration of sub-portionsof circulating ambient-adjoining convergent-divergent jetstreams in apositive feedback loop, thereby resulting in that the sub-portions ofcirculating ambient-adjoining convergent-divergent jetstreams becomemoving with de Laval M-velocities triggering alternating both: the deLaval-like jet-effect and the de Laval-like retarding-effect, therebystabilizing an effective M-velocity alternating above and below thespecific M-velocity. The disclosed aggregation of circumferentiallyarranged elemental jet-boosters as vortex generator is further used as aprincipal component of the following disclosed derivative applications:an electricity generator of high efficiency, a humidity condenser ofhigh intensity, as well as a flying-saucer of high mobility.Furthermore, the circulating sub-portions of ambient-adjoiningconvergent-divergent jetstreams become oscillating resulting inextra-intensive acoustic waves (which, when the circumferentialarrangement is regularly equidistant, become in-phase superposed therebycausing constructive interference) accompanied by the extra-enforcedwaving jet-effect, wherein the extra-increased wave power is furtherused for electricity producing.

In a further one exemplary embodiment, an aggregation of a laminar flowmaker, a pipe having an enhanced convergent-divergent jet-nozzle tunnel,and an improved wind-turbine is disclosed, representing ajet-transformer converging the heat power into the electrical power.

There has thus been outlined, rather broadly, the most importantfeatures of the invention in order that the detailed description thereofthat follows hereinafter may be better understood.

Additional details and advantages of the invention will be set forth inthe detailed description, and in part will be appreciated from thedescription, or may be learned by practice of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carriedout in practice, a preferred embodiment will now be described, by way ofa non-limiting example only, with reference to the accompanyingdrawings, in the drawings:

FIG. 1a is a prior art schematic drawing of chiral molecules;

FIG. 1b is a prior art schematic drawing of the convergent-divergentVenturi tube;

FIG. 1c is a prior art schematic view of the convergent-divergent deLaval nozzle;

FIG. 1d is a prior art schematic illustration graphics of gas velocity,static pressure, and temperature distributions within the de Lavalconvergent-divergent jet-nozzle;

FIG. 1e is a schematic drawing of a prior art ordinary blowingventilator;

FIG. 1f is a prior art schematic drawing of a body blown by an airflowportion;

FIG. 1g is a schematic drawing of a classical prior art profile of anairplane wing;

FIG. 1h is a schematic drawing of considerable amounts of water-aerosolsand micro-flakes-of-snow, which are observed behind the high-speedaircraft's wings;

FIG. 1i is a prior art schematic illustration of points of sail;

FIG. 1k is a prior art schematic illustration of a wind turbine,built-in into a cylinder;

FIG. 1l is a prior art schematic illustration of the Ranque-Hilschvortex tube;

FIG. 1m is a prior art schematic illustration of the Beverley Clock;

FIG. 2 is a prior art schematic illustration of fluid motion in animaginary flow tube;

FIG. 3 is a prior art schematic illustration of fluid motion in a realpipe;

FIG. 4 is a schematic illustration of a box having two modules;

FIG. 5a is a schematic illustration of a small portion of fluid;

FIG. 5b is a schematic illustration of a fluid small portion adjacent toa body;

FIG. 5c is a schematic illustration of a fish's squama surface fragmenthypothetical interpretation, in accordance with the principles of thepresent invention;

FIG. 5d is an illustration of a shaped body made from a hydrophobicmaterial and submerged in water;

FIG. 5e is a schematic illustration of a convex-concave corpus.

FIG. 5f is a schematic illustration of a wheel-gear-like configuredoverall shape, having a sectional profile similar to a circle-saw,comprising fragments made from a hydrophobic material;

FIG. 5g is an illustration of an exemplary aggregation comprising a setof many hydrophobic jet-gears;

FIG. 5h is a schematic isometry of a hydrophobic-propeller submerged inwater;

FIG. 5i is a schematic illustration of a hydrophobic-spiral;

FIG. 5j is a schematic isometry of a pair of hydrophobic-propellersoperating as hydrophobic-engine;

FIG. 5k is a schematic illustration of a pair of unbroken spirals;

FIG. 5l is a schematic illustration of a generalized generator;

FIG. 5m is a schematic illustration of a motionless gravity-jet engine;

FIG. 6a is a schematic illustration of an optimized convergent-divergentjet-nozzle, constructed according to the principles of the presentinvention;

FIG. 6b is a graphical representation of air velocity, static pressure,and temperature distributions along an optimized convergent-divergentjet-nozzle, constructed according to the principles of the presentinvention;

FIG. 6c is a schematic illustration of an exemplary profile of optimizedtunnel;

FIG. 6d is a schematic illustration of an exemplary profile of optimizedtunnel;

FIG. 6e is a schematic illustration of an exemplary profile of optimizedtunnel;

FIG. 6f is a schematic illustration of an optimized inverseconvergent-divergent jet-nozzle, constructed according to the principlesof the present invention;

FIG. 6g is a graphical representation of air velocity, static pressure,and temperature distributions along an optimized inverseconvergent-divergent jet-nozzle, constructed according to the principlesof the present invention;

FIG. 6h is a schematic illustration of a two-stage convergent-divergentjet-nozzle, constructed according to the principles of the presentinvention;

FIG. 7a shows comparative graphs of the dependencies of the nozzleextension ratio vs. the airflow M-velocity, calculated by the classicaland suggested models;

FIG. 7b is a schematic illustration of a compressor supplied by anoptimized convergent-divergent jet-nozzle, constructed according to theprinciples of the present invention;

FIG. 7c is a schematic sectional view of a flying capsule, constructedaccording to the principles of the present invention;

FIG. 7d is a schematic sectional view of a flying capsule, constructedaccording to the principles of the present invention;

FIG. 7e is a schematic drawing of an improved blowing propeller,constructed according to the principles of the present invention;

FIG. 7f is a schematic drawing of an improved sucking propeller,constructed according to the principles of the present invention;

FIG. 8a is a schematic illustration of an actually-airfoil wing blown bywind;

FIG. 8b is a schematic illustration of a flying airfoil body;

FIG. 8c is a schematic illustration of a flying airfoil body;

FIG. 8d is a schematic illustration of flying arranged airfoil bodies;

FIG. 9a is a schematic illustration of a sequential cascade of airfoilbodies;

FIG. 9b is a schematic illustration of an in-line cascade of ringshaving airfoil walls;

FIG. 9c is a schematic illustration of two Archimedean screws havingairfoil walls;

FIG. 9d is a schematic illustration of a circulating cascade of airfoilbodies;

FIG. 9e is a schematic illustration of airfoil rings, arrangedcircumferentially;

FIG. 9f is an adiabatic aerodynamic system comprising airfoil rings,arranged circumferentially, and wings, providing a lift-force;

FIG. 9g is a schematic drawing of an improved wind-turbine, constructedaccording to the principles of the present invention;

FIG. 9h is schematic side and front views of an improved wind-turbine;

FIG. 9i is a schematic illustration of a jet-transformer;

FIG. 10 is a schematic illustration of a block-diagram of the suggestedmethod according to the principles of the present invention; and

FIG. 11 is a table showing several equations.

All the above and other characteristics and advantages of the inventionwill be further understood through the following illustrative andnon-limitative description of preferred embodiments thereof.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The principles and operation of a method and an apparatus according tothe present invention may be better understood with reference to thedrawings and the accompanying description, it being understood thatthese drawings are given for illustrative purposes only and are notmeant to be limiting. The detailed description of the preferredembodiments is divided between two paragraphs: “Generalized Equations ofMolecular Fluid Motion” and “Jet-Effect Embodiments”, each havingsub-paragraphs.

Generalized Equations of Molecular Fluid Motion

FIG. 4 is a schematic illustration of an ideal thermo-isolated box 400,having two modules 401 and 402, separated by an ideal wall 403 having noweight, being freely-movable and easily-deformable. Thus, wall 403 mayfreely change the shapes and volume proportions of modules 401 and 402.Modules 401 and 402 are filled with portions of the same gas, having thesame static pressure P₄₀₁=P₄₀₂, but different densities ρ₄₀₁>ρ₄₀₂ andabsolute temperatures T₄₀₁<T₄₀₂, such that satisfying the conditionρ₄₀₁T₄₀₁=ρ₄₀₂T₄₀₂. It is expected that separating wall 403 will not moveand will be not deformed because the static pressures P₄₀₁ and P₄₀₂ onboth sides of wall 403 are identical. However, if wall 403 is withdrawn,then diffusion will start. This imaginary experiment says that thepresence or absence of isolating wall 403 changes the situation, and thetwo neighboring portions of gas could accelerate each other byosmotic-like pressures if the portions have the same static pressure anddiffer in density and temperature. Modelling a molecular fluid asaggregated from many stationary and moving small-portions, the describedhereinbelow interpretation of the molecular fluid portions' boundariesas sensitive to the temperature and density of surroundings as soon asthe boundaries consist of the same molecular matter as the consideredfluid, is one of the primary teachings of the present invention.

FIG. 5a is a schematic illustration of a small portion of molecularfluid, for simplicity, having the shape of a cubic portion 500. Cubicportion 500 occupies the space defined by point coordinates 501(x, y,z), 502(x+Δx, y, z), 503(x, y+Δy, z), and 504(x, y, z+Δz), where Δx, Δy,and Δz are the distances between points 501 and 502, 501 and 503, and501 and 504 correspondingly. Small portion 500 is composed of moleculesmoving randomly and in a prevalent direction, i.e. portion 500 issufficiently small, such that having no a group of molecules whirlingand making a complete rotating cycle within portion 500. Consider thecumulative force acting on portion 500. In the absence of gravitationalforces, the fluid inner-static-pressure at any point of the fluid is thesame in any direction; and the cumulative force on cubic portion 500, isdefined by the fluid inner-static-pressure change from point to point.For simplicity, let the pressure change in the direction of the x-axis505 only. The pressure on the left face, having points 501(x, y, z),503(x, y+Δy, z), and 504(x, y, z+Δz), makes the force 506 equal toP_(in)ΔyΔz, where P_(in) is the fluid inner-static-pressure at the leftface from outside of cubic portion 500; and the fluidinner-static-pressure on the opposite right face makes the force 507equal to −[P_(in)+(∂P_(in)/∂x)Δx]ΔyΔz. Therefore, the resulting force is−(∂P_(in)/∂x)ΔxΔyΔz. If one also assumes that the fluidinner-static-pressure changes in the two remaining orthogonaldirections, one can see that the pressure cumulative force per unitvolume is −∇P_(in), where ∇ is the vector differential operator. Thespatial change of the molecular fluid inner-static-pressure P_(in) mustbe considered as interrelated with the molecular fluid density ρ andabsolute temperature T variations in accordance with the thermodynamicand kinetic theory of matter.

A generalized method for modeling an equation of fluid motion,comprising consideration of momentum conservation, mass conservation,and energy conservation, wherein the fluid molecular structure is takeninto the account, is a subject of the present invention.

Inner Pressure and Momentum Conservation

Considering fluid portion 500, occupying a certain volume V, the NewtonSecond Law or the conservation of momentum says that the cumulativeforce acting on portion 500, i.e. the variation of the momentum in thevolume, must be due to the inflow or outflow of momentum through theclosed surface S of portion 500 plus the forces acting on portion 500 bythe fluid surrounding:

$\begin{matrix}{{{\frac{\partial}{\partial t}{\int{\rho\;{udV}}}} = {{- {\oint_{S}{\rho\;{{uu} \cdot {ndS}}}}} - {\oint_{S}{PndS}}}},} & {{Eq}.\mspace{14mu}(5.1)}\end{matrix}$where dS is the surface differential, n is the unit vector normal tosurface differential dS, and ρ, u, and P are functions of spatialcoordinates; wherein ρ is the fluid portion 500 density, u is the fluidportion 500 velocity-vector having absolute value u and being a measureof the molecular fluid molecules motion in a prevalent direction inaddition to the random Brownian motion, and P is thecumulative-inner-static-pressure acting on the boundaries of portion500; wherein in contrast to the classic approach of continuum mechanics,the fluid portion 500's boundaries have molecular structure, and P is asa thermodynamic parameter interrelated with the fluid temperature,density, and gravity. The kinetic theory of ideal gases defines thisrelation for a stationary case in the absence of gravity asP_(ideal)=NkT_(s)/V_(s), where P_(ideal) is the static pressure of anideal gas, V is the considered volume, N is the number of molecules inconsidered portion 500 of the ideal gas, k is the Boltzmann constant,and T_(s) is the absolute temperature of the stationary ideal gas. Theinterrelation between thermodynamic parameters in the case of ahypothetical ideal gas can also be represented by theClapeyron-Mendeleev gas law: P_(ideal)=ρ_(s)R₀T_(s)/μ, where ρ_(s) isthe stationary ideal gas density, R₀ is the universal gas constant, andμ is the molar mass of the gas. Considering a real gas, the van derWaals approach bonds the static pressure of real gas P_(Waals) acting ona stationary wall with the static pressure P_(ideal) defined in thekinetic theory of ideal gas, namely:

$\begin{matrix}{{P_{ideal} = {\left( {P_{Waals} + \frac{a}{V_{s}^{2}}} \right)\frac{V_{s} - b}{V_{s}}}},} & {{Eq}.\mspace{14mu}\left( {5.2a} \right)}\end{matrix}$where P_(Waals) is the van der Waals static pressure of real gas, actingon a stationary wall; constant b has the physical sense of excludedvolume because of the presence of the particles in the volume; andconstant a defines the attraction forces between the real gas molecules.So, the van der Waals equation of state for real gas is written as:

$\begin{matrix}{{{\left( {P_{Waals} + \frac{a}{V_{s}^{2}}} \right)\frac{V_{s} - b}{V_{s}}} = \frac{\rho_{s}R_{0}T_{s}}{\mu}},} & {{Eq}.\mspace{14mu}\left( {5.2b} \right)}\end{matrix}$

The general enough theory of molecular fluid by van der Waals isqualitatively reasonable for the liquids as well. For the purposes ofthe present patent application, the van der Waals equation (5.2b) shouldbe understood in a wider sense, allowing for the van der Waalsparameters a and b to be variable, thereby making the equation (5.2b)appropriate for rigorous quantitative calculations applied to both: realgases and liquids, and thereby, generalizing the van der Waals equationof state for a molecular fluid.

In contrast to the defined pressure P_(Waals) acting on a stationarywall, being hypothetically inert to the fluid's molecules forces, i.e.being not phobic with repulsive forces and not sticking with attractiveforces, the cumulative-inner-static-pressure P in equation (5.1) isacting on the fluid portion 500's boundaries, which, on the one hand,have the same inter-molecular attraction properties as the surroundingmatter, and, on the other hand, may be not stationary, but be subjectedto deformations and acceleration.

First, consider a static case in the absence of gravitational forces,when portion 500 is sufficiently far from a body having real walls. Inthis particular case, when portion 500, as stationary-small-portion, isnot subjected to any acceleration and is affected by a stationary-effectonly, the static pressure in equation (5.1) has the meaning of theinner-stationary-static-pressure defined for the static case. Thispressure, indicated by P_(s), as a measure of the fluid moleculescumulative stationary-impact on imaginary boundaries ofstationary-small-portion 500, is expressed as the following stationaryequation:

$\begin{matrix}{P_{s} = {P_{Waals} + {\frac{a}{V_{s}^{2}}.}}} & {{Eq}.\mspace{14mu}\left( {5.2c} \right)}\end{matrix}$Taking into the account equation (5.2c), the van der Waals equation(5.2b), written in the form expressing theinner-stationary-static-pressure, takes the following form:

$\begin{matrix}{{P_{s} = \frac{\rho_{S}r_{s}R_{0}T_{s}}{\mu}},} & {{Eq}.\mspace{14mu}\left( {5.2d} \right)}\end{matrix}$where r_(s) is the compression ratio V_(s)/(V_(s)−b), which representshow much the real fluid is compressed in comparison with a hypotheticalideal gas. For example, the assumption that the parameter b, quantifyingthe excluded volume, equals V_(s) leads to the infinite compressionratio r_(s) that corresponds to a hypothetical absolutely incompressibleliquid. Equation (5.2d) allows considering the real fluid'sinner-stationary-static-pressure P_(s) as the static pressure of theideal-like gas having specific fluid constant R_(s) defined asR_(s)=r_(s)R₀/s.

Taking into the consideration the definitions of theinner-stationary-static-pressure P_(s), compression ratio r_(s), andreal molecular fluid as the ideal-like gas having specific fluidconstant R_(s), the van der Waals equation of state for a molecularfluid, written in the form expressing theinner-stationary-static-pressure, gets the form, similar to theClapeyron-Mendeleev gas law, namely:P _(s)=ρ_(s) R _(s) T _(s)  Eq. (5.2e).In the case of an ideal gas, the sense of stationary equation (5.2e)becomes identical with the Clapeyron-Mendeleev gas law.

The value R_(s)T_(s) has the physical sense of the characteristic heatportion per unit mass, indicated by Q_(s), stored in fluidstationary-small-portion 500's molecular Brownian random motion, relatedto degrees of freedom causing the fluid molecules cumulativestationary-impact defining the inner-stationary-static-pressure P_(s),and satisfying equation (5.2e), namely: Q_(s)=R_(s)T_(s)=P_(s)/ρ_(s),and P_(s)=ρ_(s)Q_(s).

The defined pressure P_(s) can be decomposed into the following threecomponents: the static pressure P_(ideal) defined in the kinetic theoryof ideal gas, and two additive partial components defining the molecularfluid compression depending on the van der Waals parameters a and b. Thetwo additive partial components are: compression pressure-“a”, indicatedby P_(a), and compression pressure-“b”, indicated by P_(b). The indexes“a” and “b” are associated with the van der Waals parameters a and bcorrespondingly. I.e. pressure P_(s) is expressed as:P _(s) =P _(ideal) +P _(a) +P _(b)  Eq. (5.2f).

The partial compression pressure-“b” P_(b) is defined as a measure of acompression-impact-effect, caused because of increased density of themolecular fluid, sufficient to take into account the compression ratior_(s)=V/(V_(s)−b). This is a pressure deforming the shape of fluidportion 500.

The partial compression pressure-“a” P_(a) is defined as a measure of afurther deep-compression-effect, arisen because of increased density ofthe molecular fluid, sufficient to have to take into account theinter-molecular forces defined by the van der Waals parameter a,defining the potential energy of the inter-molecular attraction. Thepartial compression pressure-“a” P_(a) interrelates with the potentialenergy of the inter-molecular attraction as:

$\begin{matrix}{{U = \frac{P_{a}}{\rho_{s}}},} & {{Eq}.\mspace{14mu}\left( {5.2g} \right)}\end{matrix}$where U is the internal inter-molecular potential-energy-per-unit-mass.

Thereby:

-   -   while the molecular fluid is as an ideal gas, both: the partial        compression pressure-“a” and the partial compression        pressure-“b” equal zero: P_(a)=0 and P_(b)=0;    -   if the molecular fluid is as a solid-gas with the compression        ratio r_(s) noticeably greater than 1 and with a minor influence        of the inter-molecular attractive forces, the partial        compression pressure-“a” is marginal: P_(a)=0; and    -   if the molecular fluid is as liquid, the partial compression        pressure-“a” decisively defines potential energy of the        inter-molecular attraction.

The fluid's density, on the one hand, has the sense of a measure of thefluid molecules concentration and mass and, on the one hand, has thegravitational sense. The potential gravitational energy stored in thefluid portion unit mass in the Earth's gravitational field is G=zg,where z is the effective height of the fluid's portion above the Earth'socean surface level. Thus, the partial potential-static-pressure P_(z)distributed on height and provided by the Earth's gravitational field isadded, namely:P _(z) =zμg=ρG  Eq. (5.2),where ρ is the fluid density that in the stationary case is ρ_(s)satisfying stationary equation (5.2e).

Reference is now made to FIG. 5b , a schematic illustration of a fluidportion 510 as a generalized case of fluid portion 500 of FIG. 5a suchthat having boundaries adjacent to the stationary walls of body 511. Theapproach described referring to FIG. 5a can be further adapted to animaginary boundary layer, comprising fluid portion 510, moving near thereal walls of body 511 and being subjected to deformations andacceleration.

The adaptation involves a definition of the inner-static-pressure P_(in)provided by the fluid molecules interactions as comprising two items:P_(in)=P_(s)+P_(boundary), where P_(boundary) is the partialinner-boundary-layer-static-pressure. On the one hand, the partialinner-boundary-layer-static-pressure P_(boundary) enforces the movementto be in alignment with the adjacent stationary walls of body 511, i.e.acting as a drag, and on the other hand, it results in the fluid'sspecific velocity distribution in an imaginary boundary layer, i.e.acting as a partial pressure relating to a viscous skin-friction effect.This is formalized asP _(boundary) =P _(drag) +P _(viscous)  Eq. (5.3a),where P_(drag) is the partial drag-static-pressure acting onmoving-small-portion 510, defined as the partial pressure, which ariseswhen fluid portion 510 gets a convective acceleration redirectingmoving-small-portion 510, sliding in alignment with the curvature of thereal walls; and P_(viscous) is the partial viscous-static-pressureacting on moving-small-portion 510, defined as the partial pressure,which results in that the velocity of moving-small-portion 510 issubjected to a specific spatial distribution in the imaginary boundarylayer adjacent to the real walls of body 511. Here and further on, it isassumed that the interaction between the walls and fluid occurs withoutthe heat energy exchange between the walls and fluid, somoving-small-portion 510 is undergoing a reversible adiabatic process.

The partial drag-static-pressure P_(drag) represents either phobic, i.e.fluid-repellent pressure, interrelated with phobic-repulsive forcesdirected inward fluid portion 510, or sticking pressure, related withattractive forces directed outward fluid portion 510, when the motiontrajectory of fluid portion 510 is aligned with the wall's curvature or,more generally, with the trajectory of the adjusted portions of themoving fluid. The partial drag-static-pressure P_(drag) defines thearisen boundary level effect arising due to the curvature of the walls.The partial drag-static-pressure P_(drag) relates to the two mechanismsof fluid portion 510 acceleration: on the one hand, the partialdrag-static-pressure P_(drag) acts as a compressor-expander stagnatingfluid portion 510; and on the other hand, the partialdrag-static-pressure P_(drag) acts to change the cross-sectional area ofmoving-small-portion 510.

The effect of fluid portion 510 stagnating is formalized by the sum ofthe partial stagnation pressures: stagnation pressure-“b”, indicated byδP_(b), and of the deep-stagnation pressure-“a”, indicated by δP_(a).The indexes “a” and “b” are associated with relative variations of thevan der Waals parameters a and b correspondingly.

The partial stagnation pressure-“b” δP_(b) is defined as a measure of astagnation-impact-effect, i.e. of an effect of a cumulativestagnation-impact of the fluid molecules on the imaginary boundaries offluid portion 510. This is a pressure deforming the shape of fluidportion 510. The partial stagnation pressure-“b” δP_(b) is interrelatedwith a change of the moving-small-portion 510's volume V and, thereby,of the compression ratio r defined as V/(V−b), while retaining the sameinter-molecular forces defined by van der Waals parameter a. The valuer, now differing from the value r_(s) defined for a stationary case,specifies the partial stagnation pressure-“b” δP_(b).

The partial deep-stagnation pressure-“a” δP_(a) is defined as a measureof a further deep-stagnation-effect, observed as further deformation ofthe shape of fluid portion 510, such that resulting in quantitativechanges of the inter-molecular forces defined by the van der Waalsparameter a, allowed to be variable. If the van der Waals parameter a isassociated with the stationary-small-portion 500, subjected to thedeep-compression-effect and yet to be subjected to thedeep-stagnation-effect, then, considering the moving-small-portion 510,the variation, indicated by δa, is added, such that the van der Waalsparameter a+δa corresponds to the moving-small-portion, subjected to thedeep-stagnation-effect.

For example, while the molecular fluid is as an ideal gas, both: thepartial deep-stagnation pressure-“a” and the partial stagnationpressure-“b” equal zero: δP_(a)=0 and δP_(b)=0; if the molecular fluidis as a solid-gas with the variable compression ratio r and with minorvariations of the inter-molecular attractive forces, the partialdeep-stagnation pressure-“a” is marginal: δP_(a)=0; and by contrast, ifthe molecular fluid is liquid, the partial stagnation pressure-“b” isnegligible: δP_(b)=0.

The aspect of the partial drag-static-pressure P_(drag), associated withthe change of the cross-sectional area of moving-small-portion 510thereby providing fluid portion 510's sliding motion in alignment withthe stationary walls curvature, is formalized as the partialpressure-“c” indicated by δP_(c). The partial pressure-“c” δP_(c)interrelates with the Coanda-effect and is a measure of the cumulativealigning-impact of the fluid molecules on the imaginary boundaries offluid portion 510 moving in the imaginary boundary layer adjacent tostationary walls of body 511.

Thus, a drag-effect is the cumulative effect comprising:

-   -   the stagnation-impact-effect providing the partial stagnation        pressure-“b”,    -   the deep-stagnation-effect providing the partial stagnation        pressure-“a”, and    -   the Coanda-effect providing the partial pressure-“c”;        such that the partial drag-static-pressure δP_(drag) is        quantified as equal to the sum, comprising three items, as        expressed by:        δP _(drag) =δP _(a) +δP _(b) +δP _(c)  Eq. (5.3b).

The mentioned mechanisms, related to the partial pressures “b” and “c”,provide reversible adiabatic conversion of the kinetic energy of thefluid's molecules Brownian random motion into the kinetic energy offluid portion 510's aligned motion, and vice-versa.

The mentioned mechanism, related to the partial deep-stagnationpressure-“a”, changes the internal inter-molecularpotential-energy-per-unit-mass by a value equal to

$\begin{matrix}{{\delta\; U} = \frac{\delta\; P_{a}}{\rho_{s}}} & {{Eq}.\mspace{14mu}(5.3)}\end{matrix}$distributed in space.

The partial viscous-static-pressure P_(viscous) relates to the twomechanisms of fluid portion 510 acceleration: on the one hand, it is askin-friction effect observed as an effect of the moving fluid'smolecules sticking to the real walls; and on the other hand, it is anosmotic-like effect, which arises between the fluid's adjacent portionsdiffering in either density or temperature.

The partial skin-friction static-pressure P_(skin) is a measure, howmuch the walls are sticky for the molecular fluid motion. This can beformalized as

$\begin{matrix}{{P_{skin} = {\frac{a_{w} - a - {\delta\; a}}{V^{2}} \times {F_{skin}\left( {u,{a + {\delta\; a}},y_{w}} \right)}}},} & {{Eq}.\mspace{14mu}\left( {5.4a} \right)}\end{matrix}$where δa is the van der Waals parameter variation relative to the vander Waals parameter a associated with the stationary-small-portion yetto be subjected to the deep-stagnation-effect, V is the volume ofmoving-small-portion 510, a_(w) is the parameter similar to the van derWaals parameter a, but describing inter-attraction forces between thewalls and molecules of the fluid, i.e. the wall-fluid molecularinteraction forces; y_(w) is the distance between moving-small-portion510 and the walls; and F_(skin) (u, a+δa, y_(w)) is a function of u,a+δa, and y_(w). If the distance y_(w) is sufficiently big, theviscosity influence of the walls becomes negligible. The difference(a_(w)−a−δa) defines the effect of viscosity. When the attractive forcesbetween the walls and molecules of the fluid are stronger than thefluid's inter-molecular forces, i.e. (a_(w)−a−δa)>0, the fluid'smolecules are “sticking” to the walls, and the fluid develops viscousproperties causing the wall-fluid molecular interaction forcescumulative action against fluid portion 510's motion directionaccompanied by a dissipation of the kinetic energy of fluid portion 510into the fluid portion 510's heat energy; and when the attractive forcesbetween the walls and molecules of the fluid are weaker than the fluid'sinter-molecular forces, i.e. (a_(w)−a−δa)<0, the walls develop phobicrepellent properties. A so-called “free-slip” motion condition,corresponds to the case, when the attractive forces between the wallsand molecules of the fluid compensate the fluid's inter-molecularforces, i.e. (a_(w)−a−δa)=0.

The partial osmotic-like static-pressure P_(osmotic) defines theosmotic-like effect triggered by the gradients of density andtemperature. This can be formalized asP _(osmotic) =F _(osmotic)(a+δa,∇ρ,∇T)  Eq. (5.4b),where F_(osmotic)(a+δa, ∇ρ, ∇T) is a function of the van der Waalsparameter a allowed to be varied and of the gradients ∇ρ and ∇T. Thegradients ∇ρ and ∇T depend on the gradient of the velocity-vector ∇u. Ifall the gradients equal zero, the osmotic-like effect becomes as thediffusion caused by the Brownian random motion of the fluid's molecules.

Thus, the partial viscous-static-pressure P_(viscous) is represented asthe sum of two items, namely:P _(viscous) =P _(skin) +P _(osmotic)  Eq. (5.4c).

So, considering the general case of fluid portion 510 of FIG. 5b thatmay move either within or out of the imaginary boundary layer, thecumulative-inner-static-pressure P is interpreted as comprising thementioned items:P=P _(in) +P _(z) =P _(s) +P _(drag) +P _(viscous) +P _(z)  Eq. (5.4d),which can be further decomposed as the following:P=P _(s)+(δP _(a) +δP _(b) +δP _(c))+(P _(skin) +P _(osmotic))+P_(z)  Eq. (5.4e)The characteristic heat portion per unit mass, indicated by Q, stored influid moving-small-portion 510's molecular Brownian random motion,related to degrees of freedom causing the fluid molecules cumulativeimpact defining the inner-static-pressure P_(in), equals

$\begin{matrix}{{Q = {{RT} = \frac{P_{in}}{\rho}}},} & {{Eq}.\mspace{14mu}(5.4)}\end{matrix}$where T is the fluid moving-small-portion 510 absolute temperature that,in general, differs from the temperature T_(s) of the stationary casesatisfying the stationary equation (5.2e), and the generalized specificfluid constant R is defined for moving-small-portion 510 as R=rR₀/μ,where r=V/(V−b).

Combining equations (5.2), (5.3) and (5.4), one can derive that

$\begin{matrix}{{{Q + G} = \frac{P}{\rho}},} & {{Eq}.\mspace{14mu}(5.5)}\end{matrix}$when an adiabatic case is considered.

In a particular case, when the effect of the gravitational influence isnegligible, the cumulative-inner-static-pressure P is identical with theinner-static-pressure P_(in), and the equation of a moving molecularfluid state is derived from the equation (5.5) as:P=P _(in) =ρQ=ρRT, if P _(z)=0  Eq. (5.5a).Taking into account equation (5.5), one can rewrite integral equation(5.1) as:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int{\rho\;{udV}}}} = {{- {\oint_{S}\mspace{14mu}{\rho\;{{uu} \cdot {ndS}}}}} - {\oint_{S}\mspace{14mu}{{\rho\left( {Q + G} \right)}{{ndS}.}}}}} & {{Eq}.\mspace{14mu}\left( {5.6a} \right)}\end{matrix}$Applying Gauss's theorem to the integrals of the right part, one canspecify this as:

$\begin{matrix}{{{\frac{\partial}{\partial t}{\int{\rho\;{udV}}}} = {{- {\int{{\nabla\rho}\;{uudV}}}} = {- {\int{{\nabla{\rho\left( {Q + G} \right)}}{dV}}}}}},} & {{Eq}.\mspace{14mu}\left( {5.6b} \right)}\end{matrix}$or, in differential form:

$\begin{matrix}{{{\frac{\partial}{\partial t}u} = {{- {\nabla({uu})}} - {\nabla\left( {Q + G} \right)}}},} & {{Eq}.\mspace{14mu}(5.6)}\end{matrix}$where ∇ is the vector differential operator.

The term “∇Q” of the equation has the sense of a force per mass unitinterrelated with a change in fluid thermodynamic state, the term“∇(uu)” has the sense of an inherent convective self-acceleration offluid portion 510, and the term “∇G” has the sense of a gravitationalforce.

The momentum conservation equation in form (5.6) is applicable toviscous fluid flow being either almost incompressible as liquid orcompressible-expandable as gas. Noticing that the inner-static-pressure,in the general case, equals P_(in)+P_(in)=P_(s)+P_(drag)+P_(viscous),the exact solution of (5.6) for a steady-state flow is the Bernoullitheorem: (P_(in)/φ+(zg)+(u²/2)=Const that confirms adequateness ofequation (5.6).

Mass Conservation or Equation of Continuity

The conservation of mass says that the variation of the mass in a volumemust be entirely due to the inflow or outflow of mass through a closedsurface S of that volume, namely:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int{\rho\;{dV}}}} = {- {\oint_{S}{\rho\;{u \cdot {{ndS}.}}}}}} & {{Eq}.\mspace{14mu}\left( {5.7a} \right)}\end{matrix}$Using Gauss's theorem, one can specify this as:

$\begin{matrix}{{{\frac{\partial}{\partial t}{\int{\rho dV}}} = {- {\int{\nabla{\cdot \left( {\rho\; u} \right) \cdot {dV}}}}}},} & {{Eq}.\mspace{14mu}\left( {5.7b} \right)}\end{matrix}$and so in differential form:

$\begin{matrix}{{{\frac{\partial}{\partial t}\rho} + {\nabla{\cdot \left( {\rho\; u} \right)}}} = 0.} & {{Eq}.\mspace{14mu}(5.7)}\end{matrix}$The solution of (5.7) for a stationary case can be written as theequation of continuity: Aρu=Const, where A is the fluid flowcross-section area.Generalized adiabatic Compressibility ParameterThe mathematical equation for a hypothetical ideal gas undergoing areversible adiabatic process isP _(ideal) V ^(j)=Const  Eq. (5.8a),where j is the adiabatic compressibility-constant, defined for thehypothetical ideal gas as j=1+R₀/C_(V)=1+2/f, where C_(V) is thespecific heat capacity for constant volume, and f is the number ofdegrees of freedom per molecule of gas wherein f depends on aconfiguration of the hypothetical ideal gas molecules.

One can spread the logic of the kinetic theory of gas to define aso-called adiabatic compressibility parameter γ, now generalized for areal fluid, specifying factors reducing the degrees of freedom of thefluid's molecules. These are the compression ratio r=V/(V−b) and aninvolved function ϕ(a) of the van der Waals parameter a+δa. The involvedfunction ϕ(a+δa) has a sense of an influence of the internalinter-molecular potential-energy-per-unit-mass on the degrees of freedomof the fluid's molecules and is expressed as:

$\begin{matrix}{{\phi\left( {a + {\delta\; a}} \right)} = {\frac{P_{in}}{P_{in} - P_{a} - {\delta\; P_{a}}} = {\frac{\rho\;{RT}}{{\rho\;{RT}} - U - {\delta\; U}}.}}} & {{Eq}.\mspace{14mu}\left( {5.8b} \right)}\end{matrix}$Therefore, one can define the generalized adiabatic compressibilityparameter γ asy=1+rϕ(a+δa)R ₀ /C _(V)=1+2rϕ(a+δa)/f, i.e.y=1+rϕ(a+δa)(1−j)  Eq. (5.8c),where j now has the sense of the adiabatic compressibility parameter,defined for the real fluid, but imagined as a hypothetical ideal gascomposed of the same molecules in the assumption that the conditionsa+δa=0 and b=0 are satisfied and are interrelated to the conditionsϕ(a+δa)=1 and r=1, correspondingly. The condition γ>>1 is satisfied forliquids and ionized gases (i.e. plasma), so the following simplifiedequation becomes relevant:

$\begin{matrix}\left\{ {\begin{matrix}{\gamma = j} & {{{for}\mspace{14mu}{hypothetical}\mspace{14mu}{ideal}\mspace{14mu}{gases}}\mspace{101mu}} \\{\gamma = {1 + {r\left( {j - 1} \right)}}} & {{{for}\mspace{14mu}{real}\mspace{14mu}{gases}}\mspace{256mu}} \\{\gamma\operatorname{>>}1} & {{{for}\mspace{14mu}{real}\mspace{14mu}{liquids}\mspace{14mu}{and}\mspace{14mu}{plasma}}\mspace{104mu}} \\\left. \gamma\rightarrow\infty \right. & {{for}\mspace{14mu}{hypothetical}\mspace{14mu}{compressible}\mspace{14mu}{liquids}}\end{matrix}.} \right. & {{Eq}.\mspace{14mu}\left( {5.8d} \right)}\end{matrix}$

The definition of the generalized adiabatic compressibility parameter γallows to derive an equation for the real fluid undergoing a reversibleadiabatic process as:P _(in) V ^(γ)=Const  Eq. (5.8).

In a particular case, when the effect of the gravitational influence isnegligible, the cumulative-inner-static-pressure P becomes identicalwith the inner-static-pressure P_(in), and the equation (5.8) for thereal fluid undergoing a reversible adiabatic process can be specifiedas:PV ^(γ) =P _(in) V ^(γ)=Const, if P _(z)=0  Eq. (5.8e).

For a hypothetical ideal gas, the conditions r=1 and ϕ(a)=1 aresatisfied, and equations (5.8) and (5.8e) revert to equation (5.8a).

Energy Conservation

The conservation of energy says that the variation of the energy in avolume must be entirely due to the inflow or outflow of energy through aclosed surface S of that volume. Energy exists in many forms. In thecase, wherein portion 510 is small sufficient to have no whirling groupsof molecules, making a complete rotating cycle within portion 510 (i.e.to have no inner turbulent motions), considering a unit mass of fluidportion 510, one can take into account the following forms of theenergy:

-   -   kinetic energy K=u²/2, defined by cumulative        kinetic-energy-per-unit-mass of fluid molecules motion in a        prevalent direction;    -   potential gravitational energy G=zg, stored in the unit mass in        the gravitational field of the Earth;    -   total heat Q_(tot) as the cumulative kinetic energy per unit        mass stored in a fluid molecular Brownian random motion that for        a van der Waals gas is defined as Q_(tot)=RT×(r(j−1)), where        R=rR₀/μ. To define the total internal energy per unit mass,        indicated by U_(in), the change in degrees of freedom of the        fluid's molecules caused because of the internal inter-molecular        potential-energy-per-unit-mass U+δU is taken into the        consideration via the definition of generalized adiabatic        compressibility parameter γ, such that the total internal energy        per unit mass U_(in), is quantified as        U_(in)=Q_(tot)+U+δU=RT×(γ−1), wherein the characteristic heat        portion per unit mass Q=RT, stored in a fluid molecular Brownian        random motion, is related to degrees of freedom causing the        fluid molecules cumulative impact on the boundary surfaces of        moving-small-portion 510.

Thereby, the total cumulative energy is the volume integral of(K+G+U_(in)), wherein the advection of energy through the control volumesurface is the surface integral of ρ(K+G+Q)u·n. Thus, the conservationequation of energy is:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int{{\rho\left( {K + G + Q} \right)}{dV}}}} = {- {\oint_{S}{{\rho\left( {K + G + Q} \right)}{u \cdot {{ndS}.}}}}}} & {{Eq}.\mspace{14mu}\left( {5.9a} \right)}\end{matrix}$Using Gauss theorem one gets:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int{{\rho\left( {K + G + Q} \right)}{dV}}}} = {- {\int{{\nabla\left\lbrack {{\rho\left( {K + G + Q} \right)}u} \right\rbrack}{{dV}.}}}}} & {{Eq}.\mspace{14mu}\left( {5.9b} \right)}\end{matrix}$Since this must be valid for all control volumes V, one gets thedifferential form of the energy conservation equation:

$\begin{matrix}{{{{\frac{\partial}{\partial t}{\rho\left( {K + G + Q} \right)}} + {\nabla\left\lbrack {{\rho\left( {K + G + Q} \right)}u} \right\rbrack}} = 0},} & {{Eq}.\mspace{14mu}\left( {5.9c} \right)}\end{matrix}$or, substituting the defined expressions for the kinds of energy, it canbe written as:

$\begin{matrix}{{\frac{\partial}{\partial t}{\rho\left( {\frac{u^{2}}{2} + {z\;{\mathcal{g}}} + {RT}} \right)}} = {- {{\nabla\left\lbrack {\left( {\rho\; u} \right)\left( {\frac{u^{2}}{u} + {z\;{\mathcal{g}}} + {RT}} \right)} \right\rbrack}.}}} & {{Eq}.\mspace{14mu}(5.9)}\end{matrix}$In a stationary case, equation (5.9) can be simplified as:

$\begin{matrix}{{\nabla\left\lbrack {\left( {\rho\; u} \right)\left( {\frac{u^{2}}{2} + {z\;{\mathcal{g}}} + {RT}} \right)} \right\rbrack} = 0.} & {{Eq}.\mspace{14mu}\left( {5.10a} \right)}\end{matrix}$Comparing (5.10a) with mass conservation equation (5.7), one canconclude that

$\begin{matrix}{{\frac{u^{2}}{2} + {z\;{\mathcal{g}}} + {RT}} = {Const}} & {{Eq}.\mspace{14mu}\left( {5.10b} \right)}\end{matrix}$Taking into the account that=RT=P_(in)/ρ, one obtains the Bernoullitheorem for stationary flow:

$\begin{matrix}{{{\frac{u^{2}}{2} + {z\;{\mathcal{g}}} + \frac{P_{in}}{\rho}} = {Const}},} & {{Eq}.\mspace{14mu}(5.10)}\end{matrix}$as was predicted.

The set of specified equations (5.2), (5.3), (5.4), (5.5), (5.6), (5.7),(5.8), and (5.9) represents the generalized equations of molecular fluidmotion, the adequacy of which is confirmed by the Bernoulli theorem,equation (5.10). A method for computational fluid dynamics comprisingthe momentum conservation equation (5.6) expressed via gradient of thecharacteristic heat portion ∇Q is a subject of the present invention.

In view of the foregoing description with reference to FIG. 5b , it willbe evident to a person skilled in the art that, in contrast to thecontinuum mechanics approach based on the introduction of viscosityconstants, the description of the drag and viscosity effects bymolecular interactions defined in frames of the kinetic theory of matteris one of the primary principles of the present invention.

In view of the foregoing description with reference to FIG. 5b , it willbe evident to a person skilled in the art that the described approach,being adapted to fluid portion 510 moving near real walls of body 511,excludes the d'Alembert paradox formulated in frames of the classicalcontinuum mechanics, because of either repellent or sticking propertiesof the arisen partial drag-static-pressure P_(drag) depending on adirection of the motion velocity of fluid portion 510 and the walls'curvatures. This follows also from the kinetic theory of gas, where theterm “pressure” is defined as a measure of the random moving molecules'impact effect acting on a wall. So, considering a moving body, forsimplicity, having a spherical shape, the relative mean velocity-vectorof the impacting molecules random motion depends on the body's velocityvalue and direction, according to Galilean relativity. Thus, thedifference between the impact effects, acting on the forward and rearsides of the moving body, defines the non-zero cumulative partialdrag-static-pressure P_(drag). Furthermore, considering a moving body,having an airfoil wing-like shape triggering the Coanda-effect, thepartial pressure-“c” δP_(c), as a component of the partialdrag-static-pressure P_(drag), provides a jet-effect and, in a certaincondition, triggers the de Laval effect as described below withreference to FIG. 7c as well as with references to FIGS. 8a, 8b, 8c, 8d,9a, 9b, 9c, 9d, 9e , and 9 f.

In view of the foregoing description with reference to FIG. 5b , it willbe evident to a person skilled in the art that the partialviscous-static-pressure P_(viscous), comprising the partial skin-fictionstatic-pressure P_(skin) and osmotic-like static-pressure P_(osmotic),depends on the fluid temperature. In particular, for gases, highertemperature results in a dominant increase of the partial osmotic-likestatic-pressure P_(osmotic); and for liquids, higher temperature resultsin a decrease of the van der Waals parameter a accompanied by theskin-friction static-pressure P_(skin) decrease, primary defining thepartial viscous-static-pressure P_(viscous) decrease.

In view of the foregoing description with reference to FIG. 5a , it willbe evident to a person skilled in the art that, considering a molecularfluid in frames of the van der Waals approach, without loss ofgenerality, one can apply a modification of the van der Waals equationof state for a molecular fluid. It may be either the Redlich-Kwongequation, and/or the Berthelot model, and/or the Dieterici model, and/orthe Clausius model, and/or the Virial equation, and/or the Peng-Robinsonequation of state, and/or the Wohl equation, and/or the Beattie-Bridgmanmodel, and/or Benedict-Webb-Rubin equation as well as furthergeneralizing modifications.

In view of the foregoing description with reference to FIGS. 5a and 5b ,it will be evident to a person skilled in the art that, applying acertain resolution size of fluid portion 510 to a discrete approximationin the computational fluid dynamics, some whirling groups of molecules,i.e. some turbulent motions of fluid, become hidden within theresolution. In other words, considering a sufficiently large fluidportion 510 as a cell of the discrete approximation in the computationalfluid dynamics, the hidden turbulent motion of the groups of molecules,whirling within the fluid portion 510, is interpreted as the moleculesBrownian random motion. This means that the temperature of fluid portion510, involved into equation (5.9), should be understood in a widenedsense as a measure proportional to the average molecular kinetic energyof both: the molecules Brownian random motion and the hidden turbulentmotion of the whirling groups of molecules.

Waves in Fluid

The acoustic (elastic) wave propagating in a molecular fluid medium isdefined as a periodically oscillating motion of a molecular fluidportion with respect to the zero average Brownian distributed velocityof molecules, wherein the periodically oscillating portion is subjectedto an external energetic forced action resulting in the acoustic waveprocess.

The inventor points out that the acoustic wave process is a particularcase of the molecular fluid motion in accordance with the set ofequations (5.6), (5.7), and (5.9). The total internal energy per unitmass U_(in), comprises the portion of energy, indicated by δU_(in),which is defined as acquired from the external energetic forcedsteady-state oscillating action. The acquired portion, δU_(in), per unitmass is permanently refreshing locally and is traveling along thedirection of the acoustic wave propagation such that the total internalenergy per unit mass, U_(in), remains constant. The inventor points outthat the energy traveling (i.e. work) occurs in an adiabatic process,i.e. occurs at the expense of the internal heat energy of the molecularfluid itself. For simplicity, ignore the non-zero partialviscous-static-pressure P_(viscous) causing the irretrievabledissipation of the acoustic wave energy into the warmth of the molecularfluid medium. The set of equations (5.6), (5.7), and (5.9), inparticular, says that the wave process is a process of the energytransformation from one kind of the energy into another kind of theenergy. Namely, the kinetic energy of oscillating motion is transforminginto the potential energy interrelated with the partialdrag-static-pressure P_(drag) defined by equation (5.3b) as composed ofthree varying additive components: P_(drag)=δ P_(a)+δP_(b)+δP_(c) andaccompanied by a change of the molecular fluid density and temperatureand so interrelated with a change of the molecular fluid state in arevertible adiabatic process and, vice versa, the molecular fluidportion potential energy, interrelated with the partialdrag-static-pressure P_(drag), becomes contributed to the convectivelyacquired kinetic energy of the oscillating motion. The change in fluidstate interrelated with the oscillating motion in an adiabatic processcorresponds to a certain change in the internal heat energy of themolecular fluid, namely, ΔQ_(a)=RΔT_(a), where ΔQ_(a) is the change ofcharacteristic heat portion per unit mass, wherein the value of theadiabatic temperature change ΔT_(a)=T₂−T₁ is bonded with the varyingpartial drag-static-pressure P_(drag) by the relation:T₂/T₁=(P₂/P₁)^((γ-1)/γ), where P₁ and P₂ are the partialdrag-static-pressures P_(drag) of the subject fluid portion in twoopposite states of the oscillating portion of fluid in the adiabaticprocess, correspondingly, and γ is the generalized adiabaticcompressibility parameter as defined by equation (5.8c), wherein thevalue γ=7/5 is a good approximation for natural air as consistingdominantly of diatomic molecules.

The inventor points out that the mechanism of the adiabatictransformation between the internal heat energy and the convectivelyacquired kinetic energy of the oscillating motion is determined by theCoanda-jet-effect quantified by the partial pressure-“c” P_(c). Theadiabatic transformation between the internal heat energy and theconvectively acquired kinetic energy of the oscillating motion is inconformance with the set of equations (5.6), (5.7), and (5.9), and sothe exact solution for acoustic wave, propagating in a prevalentdirection, as a particular case of the molecular fluid steady-stateoscillating motion, is the Bernoulli theorem saying that the value(P_(in)/ρ)+(u²/2) is constant along the prevalent direction.

The inventor points out that the external energy of the forced action:

-   -   on the one hand, is a source of the wave process; as well as,    -   on the other hand, is a trigger providing for the periodically        oscillating mutual transformation of the molecular fluid        portions energy between the oscillating motion and the molecular        fluid portions internal heat energy defined by the varying        partial drag-static-pressure P_(drag), wherein the triggered        energy transformation occurs adiabatically.

This, in particular, says that the energy, brought by an acoustic wave,is composed of the external energy of the forced action and a positiveportion of energy, which is self-extracted from the internal heat energyof the molecular fluid due to the Coanda-jet-effect quantified by thepartial pressure-“c” δP_(c).

Thus, the inventor points out that the wave process is accompanied bythe Coanda-jet-effect, i.e. by a triggered effect of the molecular fluidportions convective self-acceleration, occurring adiabatically at theexpense of the internal heat energy of the ambient fluid medium.

For the purposes of the present invention, to emphasize the inherentjet-effect of the propagating acoustic wave, the term “wavingjet-effect” should be understood as a kind of the Coanda-jet-effectspecified as being applied to inner portions of a molecular fluid, as atendency of an oscillatory moving-small-portion to be attracted to andaligned with a curvature of a nearby fragment of an imaginary boundaryof a neighbor inner portion;

For the purposes of the present invention, to emphasize the jet-effectnature of the acoustic radiation pressure described hereinabove in theBACKGROUND OF THE INVENTION, subparagraph “Radiation Pressure”, the term“radiation jet-effect” should be understood as a kind of jet-effectspecified as a tendency of propagating acoustic wave to push an obstacleexposed to the propagating acoustic wave; wherein the tendency, observedas the excessive radiation pressure by the propagating acoustic wave, isinterrelated with the tendency of the acoustic wave propagation in aprevalent direction.

The inventor takes note that the terms “radiation jet-effect” and“waving jet-effect” are of interrelated senses. In other words, theinventor interprets the radiation jet-effect as aself-revealing-and-manifestation of the triggered waving jet-effectthat, in turn, is a self-revealing-and-manifestation of the triggeredCoanda-jet-effect.

Further, the inventor points out that, when the external energeticsource of an acoustic wave acts as a localized oscillator only, theacoustic wave is characterized by propagation in a prevalent direction,and, if to ignore the acoustic wave dissipation, the acoustic wavepropagation, as the wave energy traveling, occurs adiabatically. Theinventor takes note the adiabatic character of the acoustic wavepropagation allowing for a conveying the acoustic wave energy from thelocalized external energetic source of the acoustic wave to an acousticwave detector placed far from the localized external energetic source.

Interference of Acoustic Waves

The principle of superposition of waves states that when two or morepropagating waves of the same type inter-join at a point, the resultantamplitude at that point is equal to the vector sum of the amplitudes ofthe individual waves. If a crest of a wave meets a crest of another waveof the same frequency at the same point, then the amplitude is the sumof the individual amplitudes—this is constructive interference. If acrest of one wave meets a trough of another wave, then the amplitude isequal to the difference in the individual amplitudes—this is known asdestructive interference.

The inventor points out that as the acoustic waves are characterized bydominant longitudinal oscillations inherently accompanied by minorcross-sectional oscillations of a molecular fluid portion, i.e. arecharacterized by a specific field of velocities, then, considering theacoustic waves superposition, one expects the following specificself-revealing-and-manifestations of the interference, namely, when thetwo in-phase acoustic waves are joining substantially collinear, oneexpects the origination of the constructive interference;

-   -   when the two anti-phase acoustic waves are joining substantially        collinear, one expects the origination of the destructive        interference;    -   when the two identical acoustic waves are joining when        propagating in the opposite directions, one expects the        origination of a so-called standing wave as a result of the        constructive-destructive interference; and    -   when the two acoustic waves (as dominantly longitudinal waves)        are meeting when propagating in the inter-perpendicular        directions, one expects the origination of a specific kind of        interference, for the purposes of the present invention, called        an “orthogonal interference”.

In Relation to a Single Wave in a not Disturbed Molecular Fluid

When a portion of fluid is disturbed by the single acoustic wave,propagating in a prevalent direction and characterized by a certainwavelength, the fluid portion is composed of molecules:

-   -   moving randomly in all the directions with the Brownian        distribution of velocities, wherein        -   the mean squared velocity of the Brownian motion of the            molecules, equal to u_(B1), corresponding to the velocity of            the single acoustic wave propagation in the prevalent            direction in the case, and, in addition,        -   dominantly-longitudinally oscillating along the prevalent            direction, collinear to the wave propagation, with the            velocity u oscillating between the minimal value −u₁ and the            maximal value +u₁ with respect to the zero average Brownian            distributed velocity of molecules;    -   the density ρ of the portion is oscillating as interrelated with        the oscillating velocity in accordance with the equation of        continuity; wherein the inner-static-pressure and temperature of        the portion are oscillating as well as interrelated with the        oscillating density in accordance with the Van der Waals law of        the fluid state applied to an adiabatic process;    -   the wave energy U₁ per wavelength, brought by the single        acoustic wave, is equal to U₁=0.5ρ₁u₁ ², where ρ₁ is the density        of a small sub-portion of the molecular fluid, wherein the small        sub-portion having the linear size along the prevalent direction        being much lesser than a quarter of the wavelength and moving        with the maximal velocity u₁; and    -   the cross-sectional area A of any portion of fluid is        oscillating as well, according to the equation of continuity        Aρu=Const, i.e. the dominant longitudinal oscillations of a        molecular fluid portion are inherently accompanied by        cross-sectional oscillations.

In Relation to the Constructive Interference

When a portion of fluid is disturbed by two collinear in-phase acousticwaves, both characterized by the same wavelength,

-   -   at the first glance, the constructive interference is observed        as a seemingly usable energy excess when one uses a classic        detector of the usable wave energy, reacting on the fluid        molecules oscillating impact, i.e. reacting on the oscillation        of locally-excessing pressure; and    -   in a more detailed analysis, seeing that the two in-phase waves        are disturbing the fluid portions by oscillations in unison,        -   thereby superposing the fields of velocities and thereby            repeatedly reinforcing the waving jet-effect, the resulting            oscillation velocity reaches the maximal value u₊ equal to            u₊=u₁+u₂, where indexes “1” and “2” correspond to the two            in-phase waves propagating separately, and index “+”            corresponds to the case when the two in-phase waves join to            result in the constructive interference;        -   thereby causing the specifically-asymmetrical redistribution            of molecules motions degrees of freedom, the disturbed fluid            portion becomes composed by molecules, moving randomly in            all the directions with the Brownian distribution of            velocities and, in addition, oscillating in the prevalent            direction, collinear to the two in-phase waves propagations;            wherein the oscillating velocity reaches the maximal value            u₊ with respect to the zero average Brownian distributed            velocity of molecules;        -   the relative velocity increase up to u₊=u₁+u₂ is higher than            a hypothetic increase of velocity up to √{square root over            (u₁ ²+u₂ ²)}, which would be reached if considered as            limited by the cumulative energies brought by the two            in-phase waves only; wherein actually, the relative velocity            increase up to u₊=u₁+u₂ occurs also at the expense of the            internal heat energy and the corresponding established mean            squared velocity of the Brownian motion of the molecules            equals u_(B+), such that the condition u_(B+)<u_(B1) must be            satisfied in the case. Corresponding varying partial            drag-static-pressure P_(drag) interrelates with the velocity            of oscillation; and        -   the cumulative usable wave energy U₊ per wavelength, brought            by the two superposed collinear and in-phase acoustic waves,            is equal to U₊=0.5ρ₊u₊ ², where ρ₊ is the density of a small            sub-portion of the molecular fluid, wherein the small            sub-portion having the linear size along the prevalent            direction being much lesser than a quarter of the wavelength            and moving with the maximal velocity u₊, i.e.            U₊=0.5ρ₊(u₁+u₂)². For simplicity, ρ₊≈ρ₁≈ρ₂. In the case when            u₁=u₂, the cumulative usable wave energy U₊ per wavelength,            brought by the two superposed collinear and in-phase            acoustic waves, is equal to fourfold usable wave energy U₁            per wavelength, brought by a single wave, i.e. U₊=4U₁.            The inventor points out that the increase of the maximal            value u₊of the oscillating velocity with respect to the zero            average Brownian distributed velocity of molecules occurs at            the expense of the mean squared velocity of the Brownian            motion of the molecules u_(B1) (i.e. u₊<u_(B1)). This, in            particular, explains why, in a thermo-acoustic heat engine,            an acoustic resonator plays the role of a “cold sink”, and            says that the maximal value u₊is restricted by the origin            mean squared velocity of the Brownian motion u_(B1). Looking            ahead, in view of the description of subparagraph            “Convergent-Divergent Jet-Nozzle” referring to FIG. 6a of            the invention, it will become evident to a person studied            the present invention that the relative velocity u+, which            can be reached in an adiabatic waving process, is            characterized by M-velocity being lower than the specific            M-velocity, indicated by M*, specified in equation (6.9)            and, for air, estimated as of about M*≈0.5345. I.e. the            condition u₊<u_(B+)×M* must be satisfied. This condition            restricts the adiabatic increase of wave power brought by a            classic waving acoustic wave, while a shock wave may bring            higher power.            For the purposes of the present invention,    -   the term “usable wave energy per wavelength” should be        understood as a partial wave energy being proportional to the        second power of the resulting amplitude of the wave, and hence        being detectable by a classic detector of waves, reacting on the        resulting amplitude of wave; and    -   the term “enhanced waving jet-effect” should be understood as        the waving jet-effect, which is reinforced repeatedly applying        constructive interference.

In Relation to the Destructive Interference

When a portion of fluid is disturbed by two collinear anti-phaseacoustic waves, both characterized by the same wavelength, and the sameamplitude, wherein the oscillating velocities of molecules for eachacoustic wave are between ±u₁ and ±u₂, correspondingly, with respect tothe zero average Brownian distributed velocity of molecules and arealways contra-directed, i.e. providing the zero cumulative impact,

-   -   at the first glance, the destructive interference is observed as        a seemingly energy annihilation when one uses a classic detector        of wave energy, reacting on the fluid molecules oscillating        impact, i.e. reacting on the oscillation of locally-excess        pressure; and    -   in a more detailed analysis,        -   taking note that the principle of superposition, essentially            says that any complex motion can be divided into two or more            simple ones, the superposition of two fields of the two            anti-phase oscillating velocities associated with the two            anti-phase acoustic waves, correspondingly, results in a            complex field of the oscillating velocities, wherein the            complex field of the oscillating velocities hides the two            basic fields of the anti-phase oscillating velocities;        -   seeing that the two anti-phase waves are disturbing the            fluid portions by oscillations in anti-unison thereby            superposing the fields of velocities and thereby causing the            specifically-asymmetrical redistribution of molecules            motions degrees of freedom:        -   (a) the disturbed fluid portion becomes composed of            molecules moving randomly in all the directions with the            Brownian distribution of velocities and, in addition,            oscillating in the prevalent direction, collinear to the            common direction of the two anti-phase waves propagations;            wherein the velocities of molecules oscillations are            vectored in the opposite directions simultaneously within            each small volume having the linear size along the prevalent            direction being much lesser than a quarter of the            wavelength;        -   (b) the specific asymmetry of such a distribution of            velocities with respect to the directions is characterized            by hidden relative velocities in the direction of the two            anti-phase acoustic waves propagation, wherein the hidden            maximal relative velocity of anti-unison oscillating            molecules, equals u⁻=u₁+u₂, according to Galilean            relativity;        -   (c) the hidden relative velocity increase interrelates with            the corresponding varying partial drag-static-pressure            P_(drag) and defines the acquired latent energy of the            superposed acoustic waves where the latent kinetic energy is            periodically transforming into the corresponding latent            potential energy stored in the hidden stagnations; wherein            the hidden relative velocity increase up to u⁻=u₁+u₂ is            higher than a hypothetic increase of velocity up to √{square            root over (u₁ ²+u₂ ²)}, which would be reached if considered            as limited by the cumulative energies brought by the two            anti-phase waves only; wherein actually, the hidden relative            velocity increase up to u⁻=u₁+u₂ occurs at the expense of            the molecular fluid internal heat energy, and the            corresponding established mean squared velocity of the            Brownian motion of the molecules equals u_(B−), wherein the            condition u_(B−)<u_(B1) must be satisfied in the case;        -   (d) it is expected that a temperature detector, reacting on            the local thermal radiation in a prevalent direction,            perpendicular to the common direction of the two anti-phase            waves propagations, can be used for the detection of the            hidden relatively increased velocity oscillation;        -   (e) it is expected that because the velocities of molecules            oscillations being vectored in the opposite directions, the            molecules motions suffer added impedance, thus,            -   (e.1) while ignoring the added so-called wave-impedance,                the latent cumulative wave energy U⁻ per wavelength,                brought by the two superposed substantially collinear                and anti-phase acoustic waves, is equal to U⁻=0.5ρ⁻u⁻ ²,                where ρ⁻ is the density of a small sub-portion of the                molecular fluid, wherein the small sub-portion having                the linear size along the prevalent direction being much                lesser than a quarter of the wavelength and comprising                the contra-directed oscillating motions with the hidden                relative maximal velocity u⁻, i.e. U⁻=0.5ρ⁻(u₁+u₂)². For                simplicity, ρ⁻≈ρ₁≈ρ₂. In the case when u₁=u₂, the latent                cumulative wave energy U⁻ per wavelength, brought by the                two superposed substantially collinear and anti-phase                acoustic waves, is equal fourfold wave energy U₁ per                wavelength, brought by a single wave, i.e. U⁻=4U₁; and                thereby,                -   the latent cumulative wave energy of superposed                    anti-phase acoustic waves is equal to the cumulative                    usable wave energy of superposed in-phase acoustic                    waves, i.e. U⁻=U₊=4U₁ and hence, in the both cases,                    the established mean squared velocities of the                    Brownian motion of the molecules are equal, i.e.                    u_(B−)=u_(B)+, in the accordance with The Energy                    Conservation Law; and            -   (e.2) when taking into account the added wave-impedance,                that provides for a higher adequateness of the                destructive interference modelling, the increased                wave-impedance, in turn, causes a partial reflection of                the pairs of inter-superposed originally anti-phased                waves in the back direction.                For the purposes of the present invention, the term                “latent wave energy” should be understood as a form of                energy that:    -   is undetectable by a classic detector of acoustic waves,        reacting on the fluid molecules oscillating impact, i.e.        reacting on the oscillation of locally-excessing dynamic        pressure; and    -   is detectable by a thermal detector, reacting on the local        thermal radiation, wherein, in the case of the acoustic wave in        fluid (as a dominantly longitudinal wave), the thermal radiation        is dominant in a prevalent direction, perpendicular to the        common direction of the two anti-phase waves propagations.

In Relation to the Constructive-Destructive Interference as StandingWave

When a portion of fluid is disturbed by two collinearly meeting acousticwaves, both characterized by the same wavelength, and the sameamplitude, wherein the oscillating velocities of molecules for eachacoustic wave are between ±u₁ with respect to the zero average Browniandistributed velocity of molecules and are locally contra-directed,providing for a completely hidden oscillating motion with theinter-opposite velocities, and locally co-directed, providing for theresulting oscillating motion wherein the oscillating velocities ofmolecules for the resulting acoustic wave are between ±2u₁,correspondingly, the constructive-destructive interference is observedas a standing wave comprising an alternation of a seemingly energyannihilation at points, which are frequently called nodes, and aseemingly energy maximal excess at points, which are frequently calledanti-nodes.

The inventor points out that, in view of the foregoing description ofthe constructive and destructive interferences of two substantiallycollinear acoustic waves, the cumulative wave energy of the two meetingwaves is fourfold higher than the wave energy of a single wave, whereinthe wave energy is observed as usable in the anti-nodes and becomeslatent in the nodes, and wherein the acquired wave energy excess isextracted from the fluid internal heat energy due to the enhanced wavingjet-effect and so, is accompanied by the reduced established meansquared velocity of the Brownian motion of the molecules.

In Relation to the Orthogonal Interference

When a portion of fluid is disturbed by two orthogonally meetingacoustic waves, wherein the oscillating velocities of molecules for eachacoustic wave are between ±u₁ and ±u₂, correspondingly, with respect tothe zero average Brownian distributed velocity of molecules and alwaysare vectored inter-orthogonally, i.e. providing a specific superpositionof velocities oscillation, and so

-   -   for the orthogonal interference, observed as a complex acoustic        wave composed of oscillating molecules having elliptic        trajectory with the oscillating velocity of √{square root over        (u₁ ²+u₂ ²)}, the cumulative wave energy, indicated by U₀, which        is brought by the complex acoustic wave, is specified as        U₀=0.5ρ₀(u₁ ²+u₂), where ρ₀ is the density of a small        sub-portion of the molecular fluid (for simplicity, ρ₀≈ρ₁≈ρ₂),        wherein the small sub-portion having the linear size being much        lesser than a quarter of the wavelength and comprising the        orthogonally-directed oscillating motions with the relative        velocity √{square root over (u₁ ²+u₂ ²)};    -   in the case when u₁=u₂, the cumulative wave energy U₀ per        wavelength, brought by the two superposed orthogonally directed        acoustic waves, is equal double wave energy U₁ per wavelength,        brought by a single wave, i.e. U₀=2U₁.

The inventor points out that the complex acoustic wave is propagating intwo orthogonal directions and is characterized by two commensurateoscillations: longitudinal and transversal.

In relation to constructive and destructive interferences, the inventoremphasizes that, in the case of two identical, substantially collinearacoustic waves propagating in a molecular fluid, the constructiveinterference as well as destructive interference, each resulting in acomplex wave bringing the wave energy being fourfold higher than thewave energy of alone acoustic wave, wherein the energetic excess isacquired at the expense of the internal heat energy of the molecularfluid due to the enhanced waving jet-effect, and wherein the latent waveenergy of the resulting destructive interference is hidden when one usesa detector, reacting on the fluid molecules oscillating impact, i.e.reacting on the oscillation of locally-excessing pressure.

The inventor further points out that the constructive interferencecomposed of N collinear in-phase acoustic waves, each bringing waveenergy U₁, performs the resulting acoustic wave bringing the cumulativeusable wave energy U_(N), equal to U_(N)=N²U₁(of cause, while thecondition u₊<u_(B+)×M* is satisfied), wherein the energetic excess ofΔU_(N)=N(N−1)U₁ is acquired at the expense of the internal heat energyof the molecular fluid due to the enhanced waving jet-effect.

The inventor points out that, according the reciprocity theorem, if aparent acoustic wave, bringing the usable wave energy U_(N) perwavelength, is subjected to a splitting thereby forming N coherentdaughter acoustic waves, each daughter acoustic wave brings the usablewave energy U₁ per wavelength that is lower than the parent usable waveenergy U_(N) per wavelength by the factor N², wherein the lack of thewave energy, equal to ΔU_(N)=N(N−1)U₁, becomes dissipated in themolecular fluid.

Modelling an acoustic wave propagating in a molecular fluid, wherein theacoustic wave is interpreted as composed of complex motions, includingthe Brownian motion and the oscillating motion of molecules, and whereinthe two kinds of the motion storing the two kinds of energy: internalheat and wave energy, correspondingly, which are inter-transferring dueto the waving jet-effect, is one of the primary teachings of the presentinvention.

Hypothetic Electromagnetic Analogue

In relation to electromagnetic waves, according to Maxwell's equations,the electromagnetic wave energy is defined by intensity of theoscillating electromagnetic field where the electrical and magneticfields are oscillating in orthogonal planes and with the 90° phase shiftthereby providing constant electromagnetic wave energy along theelectromagnetic wave propagation path.

The inventor points out that the mentioned teaching related to acousticwaves, saying that the energy inter-transferring between the acousticwave and the molecular fluid, is hypothetically applicable to theelectromagnetic waves to solve the seemingly confusing paradoxes of theconstructive and destructive interference of the electromagnetic wavesby assuming that the electromagnetic wave interacts adiabatically withthe medium as a part of the universe, which is inherently “filled” bythe universe background matter and universe background energy (inparticular, comprising the latent energy of “electromagnetic gas”),analogously as the acoustic wave interacts with the molecular fluid.

Seeing the similarity of behaviors:

-   -   on the one hand, of propagation and interference of acoustic        waves, and,    -   on the other hand, of propagation and interference of        electromagnetic waves, for the purposes of the present        invention, the terms “waving jet-effect” and “radiation        jet-effect”, introduced hereinabove in subparagraph “Waves in        Fluid”, further should be understood in a broad sense applicable        also to the electromagnetic waves. Namely, in relation to the        electromagnetic waves:    -   the term “waving jet-effect” or “electromagnetic waving        jet-effect” should be understood as a kind of the        electromagnetic jet-effect specified as a tendency of an        electric field to be attracted to and aligned with a nearby        surface interacting with the electric field, wherein the        mentioned nearby surface is either a real conductive wall and/or        an imaginary wall formed by force-lines of the electric field        itself (i.e. it includes the interaction between nearby portions        of an oscillating electric field); and    -   the term “radiation jet-effect” should be understood as a        well-known phenomenon of electromagnetic radiation pressure,        defined in Maxwell's theory by the Poynting vector and observed        as “pushing” a conductive obstacle exposed to the propagating        electromagnetic wave, as described hereinabove in subparagraph        “Radiation Pressure”,        wherein the waving jet-effect and the radiation jet-effect, both        occur in an adiabatic process accompanied by the energy        inter-conversion between the electromagnetic wave and the        universe background energy.

For the purposes of the present invention, the term “latentelectromagnetic wave energy” or “latent electromagnetic radiationenergy” should be understood as a form of the electromagnetic energythat:

-   -   is undetectable by a classic detector of electromagnetic        radiation, reacting on the electric field oscillation, i.e.        reacting on the oscillation of locally-excessing electric and/or        magnetic field, and;    -   is detectable by a thermal detector, reacting on the local        thermal radiation, i.e. reacting on the latent electromagnetic        radiation which, when penetrating into a dense molecular body,        becomes perceptual as warmth.

The inventor notes that, while the thermal radiation is a measure of theenergetic aspect of the latent electromagnetic wave, it isself-suggested the conjecture that the perception as aroma is specifiedby the spectral aspect of the latent radiation.

In view of the foregoing understanding of the theoretical aspect of themolecular fluid motion, as headway as well as oscillating, hereinafter,several exemplary embodiments, constructed in accordance with theprinciples of the present invention and drownquintessentially-schematically, are given for illustrative purposes onlyand are not meant to be limiting, wherein the logic of applicationsusing acoustic waves is applicable to applications using electromagneticwaves.

Jet-Effect Embodiments

Fluid-Repellent Structured Surface

For the purposes of the present patent application, the term “corpus”,specified as a space-portion, bordered by a closed solid shellcontacting with ambient fluid, should be understood as a configurationalaspect of a body submerged in the fluid.

For the purposes of the present patent application, the introduced term“fluid-repellent” should be understood in a wide sense as a property ofa material to repel the fluid.

In particular, a fluid-repellent material is either:

-   -   hydrophobic, i.e. water-repellent; or    -   oleophobic, i.e. oil-repellent; or    -   so-called “omniphobic”, i.e. repelling all known liquids such as        water-based, oil-based, and alcohol-based [in particular, a        hotter surface is omniphobic]; or    -   ion-repellent, i.e. having a charged surface repulsing an        ionized gas or liquid.

The inventor points out that the term “fluid-repellent” assumes adiversity of mechanisms providing the phenomenon of hydrophobicity, forexamples:

-   -   the liquid water is diamagnetic, and so a magnet, for instance,        a permanent magnet, is interpreted as hydrophobic;    -   the phenomenon of the Archimedes extrusive force pushing up a        body floating on the surface of liquid water is interpreted as a        kind of hydrophobicity having gravitational nature; and    -   a body rotating around an own axis of rotation, for instance, a        cylinder rotating around its axis of symmetry, results in        centrifugal forces at its rotating surface, and so the rotating        surface is interpreted as omniphobic.

In view of the foregoing description with reference to FIG. 5b , it willbe evident to a person skilled in the art that the partial skin-frictionstatic-pressure P_(skin) and, hence, the partial viscous-static-pressureP_(viscous) can be controlled by choosing the body walls' material andconstructing the walls porosity, sponginess, and structure providingreduced difference (a_(w)−a−δa). For example, a bird's body is coveredby fibrous feathers and fuzz. The fibrous feathers and fuzz, making anouter surface layer constructed substantially from the air, providethat, on the one hand, the fibrous structure improves an airflowstreamlining and, on the other hand, the outer surface layer has theeffective parameter a_(w) close to the van der Waals parameter a of air(normally, the air is associated with the condition for ideal gasa+δa=0). The minimized difference (a_(w)−a−δa) minimizes the viscosityeffect of an imaginary boundary layer, and therefore, an improvedaerodynamic property of the bird's body is expected. Furthermore, thefeathers and fuzz are hydrophobic, thereby preventing the porosity fromfilling by water condensed from the natural humid air. Thereby, toweaken an undesired skin-friction effect, one can use a natural orartificial hydrophobic material, having a fibrous and porous structurecomprising many small concavities similar to feathers and fuzz orsponge, covering a surface, contacting with humid airflow. Anotherexample is that the greased feathers of a duck are water-repellent, i.e.hydrophobic, providing a free-slip condition for swimming.

FIG. 5c is a schematic illustration of yet another example of aconstructive solution, hypothetically interpreted in accordance with theprinciples of the present invention, providing compensation ofskin-friction resistance. A squama surface fragment 521 of fish 520 isshown also as an enlarged sectional view 522. Fish 520's skin 523secretes hydrophobic mucus 524 retained by fish-scales 525, having asectional profile of curved cogs. First, hydrophobic mucus 524 coversthe surfaces of fish-scales 525, forming a hydrophobic outer layer as aninherent attribute of the fish body 520's hydrodynamic-surface, whereinthe condition (a_(w)−a−δa)<0 provides for a free-slip motion. Moreover,protruding fish-scales 525 are configured and arranged such thathydrophobic mucus 524 repels a surrounding water portions 5271, 5272,5273, and 5274 with repulsive forces 5281, 5282, 5283, and 5284,correspondingly, wherein repulsive forces 5281, 5282, 5283, and 5284 actcumulatively in unison along an airfoil orientation providing for a“negative friction”. This cumulative action, dominantly, in the backwarddownstream direction provides a repulsing tendency as a kind ofjet-effect.

For the purposes of the present patent application, the terms“phobic-repulsing jet-effect”, “fluid-repellent jet-effect”, and, inparticular, the term “hydrophobic jet-effect” should be understood asthe described kind of jet-effect. A parabolic profile of mucus 524'ssurface fragment 526 provides for an enhanced hydrophobic jet-effect.Thus, both the hydrophobic outer layer and the scaly structure providethe improved hydrodynamic property of fish 520's body.

Reference is now made to FIG. 5d , showing schematically a sectionalview of a shaped wall 530, without loss of generality, orientedhorizontally. Shaped wall 530 comprises a relief-structured outer layer531, contacting with ambient water 532. Layer 531, made from ahydrophobic material, has a form of a bar with a series of teeth-likesharp and asymmetrical protrusions, thereby constituting a saw-likerelief.

In view of the foregoing description with reference to FIG. 5c , it willbe evident to a person skilled in the art that relief-structured outerlayer 531 repels adjacent portions 5371, 5372, and 5373 of surroundingwater 532 with forces 5381, 5382, and 5383 correspondingly, whereinforces 5381, 5382, and 5383 are directed dominantly horizontally. Thisprovides a hydrophobic jet-effect that can be useful for motion in thewater surrounding. In the case, wherein wall 530 is stationary, themotion of nearby portions 5371, 5372, and 5373 in the prevalentdirection [in the case, dominantly horizontal], arises at the expense ofthe repulsing interactions between the hydrophobic material and theadjacent water portions. This means that, in the final analysis, thewater portions motion in the prevalent direction occurs at the expenseof the internal heat energy [warmth] of the nearby water portions.

It will be evident to a person skilled in the art that a shape ofrelief-structured outer layer 531, contacting with surrounding water andhaving an asymmetrically saw-like configured relief, can be used fortransportation of water portions 5371, 5372, and 5373 along theasymmetrically saw-like configured relief, for example, the watertransportation along relief-structured inner walls within a capillarytube, where originating a useful hydrophobic jet-effect in addition toso-called “capillarity effect”.

FIG. 5e is a schematic illustration of a transparent-like body havingconvex-concave corpus 512. Convex-concave corpus 512 has a roundedairfoil outer convex side, and concave side 514, both contacting withambient fluid 517. A multiplicity of holes [three shown] 513.1, 513.2,and 513.3 links together both: outside portions 517.1 of the ambientfluid 517 and the ambient fluid 517's portions 517.2 contacting withconcave side 514. The concavity of side 514 has a parabolic profile withfocal point 516. Focal point 516 comprises a heating element [not shownhere], powered at the expense of either burned fuel or electricity.Thereby, hotter focal point 516 becomes omniphobic, repelling nearbyambient fluid portions 517.2 by omniphobic-repulsive van der Waalsforces. The ambient fluid molecules, subjected to theomniphobic-repulsive van der Waals forces action, acquire a prevalentcomponent of motion directed radially from the heating element at focalpoint 516 toward concave parabolic side 514. When concave parabolic side514 reflects the prevalent radial component of the molecules motion, themolecules prevalent motion component becomes collimated collinearly withsagittal axis 519, thereby forming outflowing jetstream 518. The headwaymotion of outflowing jetstream 518 provides for a jet-thrust.Furthermore, preferably, concave side 514 has outer layer 515 contactingwith ambient fluid 517.2. The layer 515 is either heated and/orimplemented from a fluid-repellent material. The parabolic profile 514of fluid-repellent outer layer 515, further acting on the fluidmolecules by phobic-repulsive van der Waals forces, partially convertsthe Brownian random component of the fluid molecules motion into amotion of the molecules in a prevalent direction toward sagittal axis519, thereby, focusing [i.e. converging] and more acceleratingoutflowing jetstream 518, in addition to the aforementioned motioncollimation.

In particular, it will be evident to a person skilled in the art thatthe body having convex-concave corpus 512, supplied with a heatingelement arranged at focal point 516, when submerged in water 517,operates as a motionless hydrophobic-engine or hydrophobic jet-gear orheating-jet engine (having a heating compressor), providing ajet-thrust, wherein one can control the jet-thrust by the heatingintensity. A net-efficiency of such a hydrophobic-engine, having aconfigured convex-concave corpus 512, is defined by the ratio of powerconsumed by the heating element to the useful kinetic power ofoutflowing jetstream 518 headway motion. The net-efficiency may comeclose to 100% if a dominant headway motion of outflowing jetstream 518is obtained by convex-concave corpus 512 shape optimization. Moreover,water portions 517.2, yet to be accumulated into outflowing jetstream518, are also subjected to a hydrophobic jet-effect, originated byparabolic fluid-repellent layer 515, resulting in an increase of theoutflowing jetstream 518 headway motion kinetic power at the expense ofthe water warms and thereby, in principle, allowing for thenet-efficiency to become even higher than 100%. Furthermore, outflowingjetstream 518 can be further subjected to a convergence by a convergentfunnel [not shown here], and thereby, become further accelerated andcooled. Thus, again, the net efficiency can exceed 100% at the expenseof the water warmth.

FIG. 5f is a schematic isometry of a body 540 having a wheel-gear-likeconfigured corpus with an overall shape, having a sectional profilesimilar to a circle-saw, constructed in accordance with an exemplaryembodiment of the present invention. Body 540 is submerged in a fluid.The configured corpus of body 540 comprises asymmetrical teeth orteeth-like fins having concave sides, which have outer layers 541, 542,543, 544, 545, 546, 547 and 548, made from a fluid-repellent material.For simplicity, the fluid is water, and the material is hydrophobic. Thehydrophobic sides 541, 542, 543, 544, 545, 546, 547 and 548 of teethrepel the water portions 551, 552, 553, 554, 555, 556, 557 and 558 withphobic-repulsive van der Waals forces 561, 562, 563, 564, 565, 566, 567and 568 correspondingly, wherein phobic-repulsive van der Waals forces561, 562, 563, 564, 565, 566, 567 and 568 are directed clockwise, alonga substantially-airfoil orientation of wheel-gear-like configured corpus540. If a hydrophobicity of the teeth sides' material is sufficientlystrong, a phobic-repulsing jet-effect, caused by phobic-repulsive vander Waals forces repelling the fluid portions, is observed. Thephobic-repulsing jet-effect provides a self-rotation of body 540 in thewater surrounding in the inverse-clockwise direction 549 at the expenseof the ambient water warmth. Thus, configured corpus 540 provides ahydrophobic jet-effect, accompanied by cooling of the ambient water.Moreover, if the effective diameter 5401 of wheel-gear-like configuredcorpus 540 is big sufficiently, the momentum of the rotating forcesbecomes perceptible, according to the Archimedes' theory of lever.

For the purposes of the present patent application, the term“fluid-repellent jet-gear”, having a widened sense, is introduced asrelating to a body submerged in a fluid, wherein the body corpus has anasymmetrically configured relief having an airfoil orientation and alayer contacting with the ambient fluid, wherein the layer is eithermade from a fluid-repellent material and/or comprising a heating elementmaking the layer omniphobic, and wherein the configured relief of the“fluid-repellent jet-gear” corpus comprises asymmetrical protrusions,for example, teeth-like fins, or humps, or screwed blades, orconvex-concave elements. The asymmetrical corpus is oriented such thatthe protrusions' fluid-repellent sides repel the fluid portions in aprevalent direction along the corpus airfoil orientation. In aparticular case, the fluid is water, the fluid-repellent material ishydrophobic, and the term “hydrophobic jet-gear” or “hydrophobic-engine”is used.

In view of the foregoing description with reference to FIGS. 5c, 5d, 5e,and 5f , it will be evident to a person skilled in the art that thedescribed specifically constructed outer layer of a fluid-repellentjet-gear corpus, contacting with the ambient fluid, is characterized bythe following principle features: the outer layer comprises at least onefragment, being fluid-repellent, and that the fluid-repellent fragment'sshape is asymmetrical relative to the direction of fluid motion, suchthat the fluid-repellent fragment repels the fluid portions in aprevalent direction along an airfoil orientation of the corpus. In thecase wherein the prevalent direction is dominantly the same as thedirection of the fluid motion, such a constructive solution compensatesa skin-friction resistance. As well, it will be evident to a personskilled in the art that the described phobic-repulsing jet-effect ismore powerful, if either the repulsive forces of the fluid-repellentmaterial are stronger, and/or the fluid-repellent fragments of thefluid-repellent jet-gear's outer layer occupy a bigger area contactingwith the ambient fluid, and/or the fluid-repellent fragment shapes areoptimized to enhance the prevalent directivity of the phobic repelling.Thereby, constructive solutions, providing developed surface offluid-repellent fragments resulting in an increased phobic-repulsingjet-effect, can provide that the increased phobic-repulsing jet-effectbecomes stronger than a skin-friction resistance effect and, thereby,enables the fluid-repellent jet-gear motion at the expense of the nearbysurrounding fluid matter warmth only, i.e. in an adiabatic process, thefluid portions, adjacent to the fluid-repellent jet-gear, become colderthan the fluid portions, yet to be subjected to the phobic-repulsingjet-effect.

In view of the foregoing description with reference to FIG. 5f , it willbe evident to a person skilled in the art that:

-   -   a so-called Peltier-element can be adapted to operate as a        thermoelectric generator producing electricity at the expense of        the temperature difference between water portions subjected and        not-subjected to the described hydrophobic jet-effect; and    -   if the ambient fluid is plasma, i.e. an ionized gas or liquid,        then an electrically charged surface, repulsing ions of the        ionized fluid by electrostatic forces, functions as a        fluid-repellent material. In another example, a surface, being        hotter than ambient fluid, functions as a fluid-repellent        material.

FIG. 5g is a schematic top view of an exemplary aggregation 5600comprising a set of many hydrophobic jet-gears submerged in water. Thehydrophobic jet-gears, similar to body 540, described hereinbefore withreference to FIG. 5f , arranged in-lines and in-columns, without loss ofgenerality, in a horizontal plane. In a more general case, also,aggregation 5600 comprises several such horizontal layers, one above theother, that are not shown here. Aggregation 5600, occupying length 5601and width 5602, for simplicity, each equal to L, and height, equal to Hand comprising several horizontal layers. Dashed curves 5603 symbolizethat a number of the lines and columns is substantially greater thanshown. A fragment of aggregation 5600 is shown also as an enlarged view560, where neighbor opposite hydrophobic jet-gears 5610 and 5620 differin directivity of corpuses' overall airfoil orientation and, inparticular, in directivity of asymmetrical teeth having hydrophobicouter layers 5613 and 5623 correspondingly. Hydrophobic jet-gears 5610repel water portions 5614 with forces 5615, directed clockwise, andhydrophobic jet-gears 5620 repel water portions 5624 with forces 5625,directed inverse-clockwise. Thereby, the neighbor opposite hydrophobicjet-gears 5610 and 5620 repel adjacent portions of surrounding water inunison. Aggregation 5600, comprising the multiplicity of relativelysmall hydrophobic jet-gears 5610 and 5620, provides increased cumulativearea of hydrophobic outer layers 5613 and 5623 contacting with water.Thereby, the hydrophobic jet-gears 5610 and 5620 of aggregation 5600 aresubjected to a cumulative phobic-repulsing jet-effect that can beestimated for the exemplary arrangement as the following. An exemplaryhydrophobicity of a hydrophobic material is characterized by ahydrophobic pressure of P_(h)=0.5 Pa. Imaging a practicallyimplementable hydrophobic jet-gears 5610 and 5620 having an effectivediameter of D=1 cm, and comprising 8 teeth, each of gap 5604 d=1.25 mm,and thickness 5605 equal to h=2 mm, one estimates that thehydrophobic-repulsive force per one hydrophobic jet-gear 5610 or 5620equals F_(h)=P_(h)×8×d×h=0.5×8×1.25×10⁻³×2×10⁻³=10⁻⁵N. On the otherhand, one defines the fluid resistance force, indicated by F*_(drag), inthe frames of continuum mechanics as F*_(drag)=(6πη×r)u_(t), where r isso-called Stokes's radius, u_(t) is the velocity of a body relative tothe considered viscous fluid, and η is the dynamic viscosity of fluid.The dynamic viscosity of water at 20° C. is approximately of r=10⁻³Pa×sec. In the case of rotating hydrophobic jet-gears 5610 and 5620, thevalue r is estimated approximately, as r≈h/2, thus, the fluid resistanceforce F*_(drag) per one hydrophobic jet-gear 5610 or 5620 is estimatedas F*_(drag)≈2×10⁻⁵u_(t), wherein the velocity u_(t) means the effectivetangential velocity of rotating teeth 5613 and 5623. The conditionF_(h)=F*_(drag) defines the reachable effective tangential velocityu_(t) for the case of no-loaded rotation. So, the hydrophobic-repulsiveforce F_(h)=10⁻⁵N can provide a relatively fast no-load rotation ofhydrophobic jet-gears 5610 and 5620 corresponding to the effectivetangential velocity of teeth 5613 and 5623, equal tou_(t)=F_(h)/(2×10⁻⁵)≈0.5 m/sec.

Consider an electricity generator producing useful electricity from thesurrounding water warmth, wherein either a subset, composed ofhydrophobic jet-gears 5610, and/or a subset, composed of hydrophobicjet-gears 5620, powers a rotor of the electricity generator. If therotation of hydrophobic jet-gears 5610 and/or 5620 is loaded by theelectricity generator resulting in the loaded rotation corresponding tothe effective tangential velocity of teeth 5613 and/or 5623 equal tou_(h)=1 m/sec, then the rotation power W_(h), produced by thehydrophobic-repulsive force F_(h), is of aboutW_(h)=(F_(h)−F*_(drag))×u_(h)≈10⁻⁵ W.

A parallelepiped having the horizontal area L×L of 10×10=100 m², and thevertical height of H=1000×h=2 m, can comprise about n=10⁹ hydrophobicjet-gears 5610 and 5620 producing the cumulative hydrophobic power ofabout n x W_(h)=10 kW. Thereby, such a relatively compact aggregationoccupying a volume of 200 m³ can produce an industrial amount ofelectricity from permanently refreshed warm water. Furthermore, takinginto account that the heat of fusion coefficient for water is 335 kJ/kg,the cumulative hydrophobic power of 10 kW, when reduced from waterwarmth in favor of electrical power, at the same time, allows forcrystallization of ice from seawater (i.e. allows for operation as anice-maker) and thereby enables harvesting of desalinated water, whereinproviding an industrial amount of potable water of about 100 kg/hour.

In view of the foregoing description with reference to FIG. 5g , it willbe evident to a person skilled in the art that:

-   -   a hydrophobic surface submerged in water operates as a cooler        (analogously as the “cold sink” in the aforementioned example        with the Beverley Clock described hereinabove in subparagraph        “Phenomenon of Hydrophobicity and the Beverley Clock” with the        reference to FIG. 1m );    -   one could implement an electricity generator comprising an        aggregation of fluid-repellent jet-gears and Peltier-elements        operating as thermoelectric generators producing electricity at        the expense of the temperature differences caused by the        phobic-repulsing jet-effect; and    -   an electricity generator, turbo-electric or thermoelectric,        comprising an aggregation of hydrophobic jet-gears could operate        efficiently if the surrounding warm water is permanently either        refreshed and/or consuming caloric; as well,    -   aggregation 5600 of equidistantly arranged hydrophobic        jet-gears, provides for constructive interference of many        in-phase superposed acoustic waves.

FIG. 5h is a schematic isometry of a fluid-repellent propeller 570submerged in the fluid. For simplicity and without loss of generality,describe fluid-repellent propeller 570 submerged in the fluid ashydrophobic-propeller 570 submerged in water surroundings.Hydrophobic-propeller 570 has asymmetrically screwed and orientedairfoil blades 571. For simplicity, consider a case, when asymmetricalairfoil blades 571 forcedly remain stationary. One of the primaryfeatures of hydrophobic-propeller 570 is that asymmetrically screwed andoriented airfoil blades 571, constructed in accordance with an exemplaryembodiment of the present invention, have at least one side, withoutloss of generality, frontal side 573, having a layer, made from astrongly-hydrophobic material. As described hereinabove referring toFIGS. 5c, 5d, and 5f , this feature triggers a hydrophobic jet-effectand, thereby, originates a motion of the water sub-portions formingsub-streams 575 having the motion headway component, co-directed withsagittal axis 574, and a whirling component, caused by airfoil blades571 asymmetries. To reduce distortions and micro-turbulences ofsub-streams 575, another side of asymmetrical airfoil blades 571, hiddenin FIG. 5h , is made from a weakly-hydrophobic material and/or has afibrous and porous layer, making the layer as composed of micro-portionsof water held in the pores, thereby, minimizing the difference(a_(w)−a−δa) and, hence, reducing the skin-friction resistance. Assumingan exemplary hydrophobicity of the strongly-hydrophobic material,characterized by a hydrophobic pressure of P_(hp)=0.5 Pa, andconsidering an implementable small size of hydrophobic-propeller 570,namely, the effective diameter D_(hp)=1 cm, one can estimateapproximately that:

-   -   on the one hand, the hydrophobic-repulsive force per one        hydrophobic-propeller 570, indicated by F_(hp), equals        F_(hp)=P_(hp)×0.25π×D_(hp) ²F=P_(hp)×0.25π×D_(hp)=1.25π×10⁻⁵N;        and    -   on the other hand, the fluid resistance force per one        hydrophobic-propeller 570, indicated by F**_(drag), is estimated        in frames of the classical hydrodynamics as F**_(drag)=(6πη×        r_(hp)) u_(hp), where r_(hp) is so-called Stokes's radius,        chosen for the case as r_(hp)=D_(hp)/2, u_(hp) is the effective        local tangential velocity of sub-streams 575 relative to blades        571, and η is the dynamic viscosity of fluid. The dynamic        viscosity of water at 20° C. is approximately of η=10⁻³ Pa×sec.        The condition F_(hp)=F**_(drag) defines the reachable effective        velocity U_(hp). So, the hydrophobic-repulsive force F_(hp) can        provide a relatively fast motion of sub-streams 575 with the        effective local tangential velocity U_(hp), equal to        u_(hp)=F_(hp)/(6πη×r_(hp))≈0.42 m/sec. One can translate the        effective local tangential velocity u_(hp), into the effective        velocity u₅₇₄ of sub-streams 575 headway motion along sagittal        axis 574. The translation depends on the effective angle β_(hp)        of asymmetrically screwed and oriented blades 571 slope relative        to sagittal axis 574. The interrelation is u₅₇₄=u_(hp)        Cos(β_(hp)). For instance, u₅₇₄≈5 cm/sec for β_(hp)=83°. The        headway motion velocity u₅₇₄ defines the hydrophobic headway        repelling power per one small hydrophobic-propeller 570 as        W_(hp)=F_(hp)u₅₇₄, estimated approximately as W_(hp)≈2×10⁻⁴ W.

In view of the foregoing description with reference to FIG. 5h , it willbe evident to a person skilled in the art that:

-   -   the hydrophobic pressure pushes a water portion, which further        is subjected to elastic reaction by the ambient water, and so,        in addition to the directional jet-thrust, the action generates        also a peculiar shock-like acoustic wave propagating in the        water medium and being characterized by a peculiar frequency and        peculiar wavelength. In particular, an acoustic wave having a        chiral circumferential polarization is expected in the case, and        hydrophobic-propeller 570 can be interpreted as a source of the        peculiar shock-like acoustic wave; and    -   the described logic, applied to hydrophobic-propeller 570        submerged in water and thereby launching water sub-streams 575,        is applicable to a propeller, similar to hydrophobic-propeller        570, but having frontal surfaces 573 comprising an outer layer,        being electrically charged instead of hydrophobic, and being        submerged in an ionized gas, and thereby functioning making        sub-streams 575 of the ionized gas.

FIG. 5i is a schematic illustration of a stationary spiral 576 submergedin a fluid. Spiral 576 has helically coiled elaborated airfoil-profiledwalls, constructed in accordance with an exemplary embodiment of thepresent invention. The outer surface 577 of spiral 576, is covered by afluid-repellent material. Without loss of generality, the fluid is waterand the material, covering outer surface 577, is hydrophobic, and so,spiral 576 is hydrophobic as well. Such a configuration, acting on thewater surroundings by phobic-repulsive van der Waals forces, creates ahelically outflowing water jetstream 578, i.e. having two components ofmotion, namely: headway along sagittal axis 579 and whirling. The motionoccurs at the expense of the internal heat energy of water. Thestationary hydrophobic spiral 576 can be interpreted as ahydrophobic-engine lunching jetstream 578.

Exemplary Implementation of Constructive Interference

The inventor points out that each ring of spiral 576 acts as a source ofa peculiar shock-like acoustic wave, while each pair of the neighborrings acts as a source of a forced elemental acoustic wave. Furthermore,the sequential in-line arranged pairs of the neighbor rings of spiral576, acting as an array of sources, generating a multiplicity of theforced elemental acoustic waves, which form a spatial interference withrespect to the system of coordinates linked to moving flow 578. Wherein,when, in general, a varying pitch of spiral 576 is especially adapted tothe acceleration of water portions, the multiplicity of the forcedelemental acoustic waves provides constructive interference where allthe forced elemental acoustic waves become superposed in-phase alongaxis 579. For the sake of clarity, there are N rings in spiral 576originating N forced elemental acoustic waves, correspondingly. Theresulting acoustic wave, formed by the superposition of the N forcedin-phase elemental acoustic waves, brings the resulting wave powerproportional to the second power of the resulting wave amplitude. Hence,the cumulative usable wave power of the resulting acoustic wave ishigher than the sum of powers of the elemental acoustic waves by thefactor of N², wherein the self-acquired portion of the resulting wavepower is self-extracted from the internal heat energy of the ambientwater due to the multi-stage repeated waving jet-effect as describedhereinabove in subparagraph “Interference of Acoustic Waves”.

It will be evident to a person skilled in the art that a long screw,similar to stationary hydrophobic spiral 576, can be interpreted as ahydrophobic-oscillator launching acoustic beam 578. As well, thementioned aggregation 5600 (FIG. 5g ) of equidistantly arrangedhydrophobic jet-gears, provides for constructive interference of manyin-phase superposed acoustic waves.

The inventor points out to the legendary story about Tesla's mechanicaloscillator, claimed extra-powerful acoustic wave generation of whichbecomes believable in view of the foregoing description.

In contrast to the resonance scheme by Tesla, the proposed superpositionof N in-phase acoustic waves (wherein N is a specified number), toprovide for the desired constructive interference bringing usable wavepower, is easily controllable.

It will be evident to a person skilled in the art that the long screwsupplied with an acoustic wave power detector as a power converter iscapable of operating as an electricity generator producing electricityfrom the water warmth due to the hydrophobic jet-effect and the enhancedwaving jet-effect.

In view of the foregoing description with reference to FIGS. 5c, 5d, 5f,5g, 5h, and 5i , it will be evident to a person skilled in the art that:

-   -   hydrophobic-propeller 570 and hydrophobic spiral 576 can be        interpreted as kinds of a fluid-repellent jet-gear, where        asymmetrically screwed and oriented airfoil blades are used        instead of primitive teeth-like fins; and    -   one can implement fluid-repellent jet-gears of various        configurations, for example, having an overall shape in a form        of either a saw, or a circle-saw, or a spiral staircase, or a        propeller, or a screw of Archimedes.        Rational Explanation of Origin of Life

In view of the foregoing description with reference to FIG. 5i , wherean asymmetrical spiral, having a form of the Archimedean screw andhaving a hydrophobic surface, originates a helical motion of fluid, oneexpects that, contrariwise, if the asymmetrical spiral, having ahydrophobic surface, is decomposed into many separate chiral particleshaving a hydrophobic side and being submerged in water, where beingarranged and oriented randomly, like a suspended matter, then the water,forcedly and certainly helically-flowing around the separate chiralparticles, has a predominance to organize the chiral particles into thementioned asymmetrical spiral in the form of the Archimedean screw,while other particles, geometries of which are not in a conformance withthe water motion, remain not organized into a spiral. Thus, inaccordance with the principles of the present invention, a mechanism,providing a regularized aggregation of separate left-handedstereoisomers of amino acids into a coiled sequence thereby forming aribonucleic acid (RNA) molecule, hypothetically, can be specified andimplemented artificially. Furthermore, a certain, forced spatialdistribution of water flow velocities can provide for that right-handedstereoisomers of amino acids become aggregated in an orderly manner intoa nonexistent inversely-screwed right-chiral molecule, which ismirror-symmetrical to a natural RNA.

Reference is now made to FIG. 5j , a schematic illustration of a pair ofhydrophobic-propellers: 570 and 580. Hydrophobic-propeller 570 is thesame as shown and described hereinabove referring to FIG. 5h . Allreference numerals 571, 573, 574, and 575 are the same as describedreferring to FIG. 5h . Hydrophobic-propeller 580 has stationary airfoilblades 581, asymmetrically screwed and oriented relative to sagittalaxis 584. An imaginary compound of blades 571 and sagittal axis 574 ismirror-symmetrical to an imaginary compound of blades 581 and sagittalaxis 584. The chiral compounds are arranged sequentially such thatsagittal axes 574 and 584 are collinear. Analogous to the case of blades571, frontal side 583 of blades 581 is covered with a layer, made from astrongly-hydrophobic material; while, to reduce distortions andmicro-turbulences of sub-streams 585, another side of asymmetricalairfoil blades 581, hidden in FIG. 5h , is made from aweakly-hydrophobic material and/or has a fibrous and porous layer,making the layer, contacting with ambient water, as composed ofmicro-portions of water held in the pores, thereby, minimizing thedifference (a_(w)−a−δa) and, hence, reducing the skin-frictionresistance. Airfoil blades 581, triggering the hydrophobic jet-effect,accelerate the water sub-portions forming sub-streams 585 having themotion headway component, co-directed with sagittal axis 584, and awhirling component. As asymmetrical blades 571 and 581 aremirror-symmetrical, the whirls of sub-portions 575 and 585 are inmutually-opposite directions; and as sub-streams 585 are thedownstream-continuations of sub-streams 575, the whirls of sub-streams575 and 585 become mutually-suppressed. Thus, the chiral compounds,being mutually complemental and pushing water forward, create resultingjetstream 588, having dominant headway motion originated by the bladesfrontal sides hydrophobicity and at the expense of the water warmth. Thepair of chiral hydrophobic-propellers 570 and 580 can be considered as awhole and be interpreted as hydrophobic-device 590 lunching jetstream588. Wherein the power, indicated by W₅₈₈, of jetstream 588, launched bysmall hydrophobic-device 590, having the effective diameter D=1 cm, ishigher than 2W_(hp), because the mutually-suppressed and thereforereduced power of sub-streams 575 and 585 whirls is at least partiallytransformed into the power of jetstream 588 headway motion.

The inventor points out that the pair of chiral hydrophobic-propellers:570 and 580 generates a forced elemental acoustic wave with thewavelength equal to the distance between the chiralhydrophobic-propellers: 570 and 580 along sagittal axis 574. It will beevident to a person skilled in the art that a multiplicity of in-linecascaded pairs of chiral hydrophobic-propellers: 570 and 580 causes asan accelerated jetstream as well as interference of the forced elementalacoustic waves, and using an adapted pitch between and within the pairs,a controlled interference: either constructive and/or destructive,becomes applicable.

FIG. 5k is a schematic illustration of a stationary pair of unbrokenchiral spirals having shapes of the Archimedean screws, briefly, screws592 and 593 having helically coiled airfoil-profiled walls, constructedin accordance with an exemplary embodiment of the present invention.Screws 592 and 593 have a common sagittal axis 594 and differ indirection of coiling: clockwise and inverse-clockwise from a frontalpoint of view. Chiral screws 592 and 593 are submerged in a fluid. Theouter surfaces 596 and 597 of chiral screws 592 and 593,correspondingly, are covered by a fluid-repellent material. Without lossof generality, the fluid is water and the material, covering outersurfaces 596 and 597, is hydrophobic. Such a configuration, acting onthe water surroundings by phobic-repulsive van der Waals forces, createsan outflowing water jetstream 595 moving dominantly along sagittal axis594, wherein the whirling component of the motion is suppressed. Again,the motion occurs at the expense of the water warmth. The stationarypair of chiral screws: 592 and 593, can be considered as a whole and beinterpreted as a hydrophobic-device 591 lunching jetstream 595.

In view of the foregoing description with reference to FIGS. 5h, 5i, 5j,and 5k , it will be evident to a person skilled in the art thathydrophobic-device 590 and/or 591 can be supplied with a Peltierelement, capable of operating as a thermoelectric generator producingelectricity from the temperature difference caused by the hydrophobicjet-effect. As well, if asymmetrical airfoil blades 571 and/or 581and/or 592 and/or 593 are capable of rotation, then thehydrophobic-repulsive force F_(hp) results in rotations of theasymmetrical airfoil blades, and hydrophobic-propellers 570 and 580, aswell as hydrophobic-devices 590 and/or 591 can be applied to electricitygeneration using a turbine-generator.

In view of the foregoing description with reference to FIGS. 5e, 5h, 5i,5j, and 5k , it will be evident to a person skilled in the art thathydrophobic-devices 512 and/or 590 and/or 591 can be cascadedsequentially and in-parallel, and a big submarine can be supplied withan aggregated jet-device, composed of many small hydrophobic-devices 512and/or 590 and/or 591 and thereby providing a substantial cumulativejet-thrust.

The pair of chiral screws: 592 and 593 generates a forced resultingacoustic wave propagating along sagittal axis 594. The forced resultingacoustic wave is composed of elemental acoustic waves originated by eachring of the screws.

The inventor points out that a long screw, either alone as screw 576shown in FIG. 5i , or combined as the pair of screws: 592 and 593,constructed to provide an in-phase superposition of a big number N ofgenerated elemental acoustic waves, results in the constructiveinterference forming a combined acoustic wave, bringing the usable wavepower that higher than the usable power of one elemental acoustic waveby the factor of N².

Aerodynamic and Hydrodynamic Effects

In view of the foregoing description with reference to FIGS. 4, 5 a, 5b, 5 c, 5 d, 5 e, 5 h, 5 i, 5 j, and 5 k, it will be evident to a personskilled in the art that, considering flow as moving molecular fluid,when a flow portion is flowing around a body, the flow portion and bodybecome subjected to the following main aerodynamic and hydrodynamiceffects, differing in mechanism of originating:

-   -   stagnation of the flow portion impacting the body resulting in        drag of the body;    -   sticking of the flow portion to the body resulting in        skin-friction;    -   attracting and thereby redirecting of the flow portion to a        smoothly curved body surface, i.e. the Coanda-effect as a kind        of jet-effect, resulting in a lift-force acting on the body;    -   convective (i.e. jet-effect) self-acceleration, resulting in        jet-thrust acting on the body, wherein the jet-thrust is        vectored against the flow portion acceleration and hence,        against the flow portion headway motion;    -   an adiabatic compression and/or extension acting on the body by        the static pressure and temperature variations, both changing        adiabatically;    -   the turbulence of the flow portion, swirling and vibrating the        body and ambient surroundings;    -   diffusion, interrelated with the osmotic-like partial pressure,        resulting in penetrating the flow portion into the ambient        molecular fluid and, vice-versa, in entrapping the ambient        molecular fluid by the flow portion (this effect is also        frequently called the Coanda-effect);    -   hydrophobicity of the body, resulting in repelling the flow        portion and thereby originating the hydrophobic jet-effect; and    -   peculiar and forced oscillation of fluid portions, both being        interrelated with the waving jet-effect and resulting in        peculiar and forced acoustic waves, correspondingly.        All the effects contribute in the        cumulative-inner-static-pressure acting on the boundaries of the        flow portion. As the effects differ in mechanism of originating,        the proportion of the mentioned effects action intensity may        vary, depending on both: a geometry of the body and a velocity        of the flow. In a certain situation, when the body has an        airfoil shape, the component of jet-thrust may exceed the drag        and skin-friction, thereby providing a positive net jet-thrust        against the flow, as it occurs, for example, with a sailboat,        when a point of sail belongs to the “close-hauled” group “B”, as        described hereinabove with reference to FIG. 1i . As well, the        generated as peculiar as well as forced acoustic waves, when        superposed, constitute interference, the resulting wave power of        which is acquired from the fluid warmth due to the waving        jet-effect.        Electromagnetic Accompanying

Reference is now made again to FIG. 5i , wherein now, the ambient fluidis a water-based electrolyte.

The inventor points out that, in this case, each ring of spiral 576,acting as a source of a peculiar acoustic wave, generates also as apeculiar electromagnetic wave, as well, each pair of the neighbor ringsacts as a source of a forced elemental electromagnetic wave.Furthermore, the sequential in-line arranged pairs of the neighbor ringsof spiral 576 acts as an array of sources, generating a multiplicity ofthe forced elemental electromagnetic waves, which form spatialinterference. For the sake of clarity, there are N rings in spiral 576originating N forced elemental electromagnetic waves, correspondingly.Considering the elemental electromagnetic waves propagating along axis579 only, when a pitch of spiral 576 is equidistant and therebyproviding a certain time-delay interrelated with a phase-shift betweenthe forced elemental electromagnetic waves, the multiplicity of the Nforced elemental electromagnetic waves forms a constructive interferencealong the axis 579, where all the N forced elemental electromagneticwaves become superposed in-phase.

The resulting electromagnetic wave, formed by the superposition of theforced in-phase elemental electromagnetic waves, brings the resultingusable wave power proportional to the second power of the resultingamplitude of the oscillating electric field. Hence, the cumulativeusable wave power of the resulting electromagnetic wave is higher thanthe usable wave power of one elemental electromagnetic wave by thefactor of N² and is higher than the sum of usable wave powers of all theN elemental electromagnetic waves by the factor of N, wherein theself-acquired portion of the resulting electromagnetic wave power isself-extracted from the universe background energy (at least from theelectromagnetic gas heat-like energy) stored in the space due to theelectromagnetic waving jet-effect as described hereinabove:

-   -   in relation to an electric flux, with the reference to prior art        FIG. 1f , and    -   in relation to an electromagnetic wave, in subparagraph        “Hypothetic Electromagnetic Analogue”.

The inventor points out that a specifically arranged sequence of sourcesof acoustic waves in an electrolyte that, in the final analysis, is thespecifically arranged sequence of sources of elemental electromagneticwaves (for instance, similar to spiral 576 representing a helicalantenna launching chiral circularly-polarized radio waves), whensupplied with a detector of the resulting electromagnetic wave power asa power converter which is capable of transformation of theelectromagnetic wave power into electrical power, becomes capable ofoperating as a generator of electricity, producing the electrical powerfrom the universe background energy stored in the space occupied by theelectrolyte due to the electromagnetic waving jet-effect.

Generalized Generator of Useful-Beneficial Power

The foregoing description, expound hereinabove in subparagraphs:

-   -   “Exemplary Implementation of Constructive interference”,        proposing a generator of electricity capable of producing the        electrical power from the ambient warmth due to the acoustic        waving jet-effect; and    -   “Electromagnetic Accompanvinq”, proposing a generator of        electricity capable of producing the electrical power from the        universe background energy due to the electromagnetic waving        jet-effect;        both with reference to FIG. 5i , is further summarized        hereinbelow as a description of a generalized generator for        producing a useful-beneficial power, constructed according to        the principles of the present invention to harvest the        useful-beneficial power from at least one of:    -   the ambient warmth, in relation to the mechanic power of a        moving molecular fluid and acoustic waves; and    -   the universe background energy, in relation to the        electromagnetic power of electromagnetic waves.

FIG. 5I is a schematic illustration of the generalized generator 5.00for producing the useful-beneficial power, constructed in accordancewith the principles of the present invention.

For the purposes of the generalization, a set of interrelated terms aredefined as follows:

-   -   (a) peculiar shock-like wave is defined as a reaction originated        by a local acceleration of a fluid portion in a prevalent        direction and as a peculiar wave, propagating in the accelerated        headway-moving portion of fluid;    -   (b) an elemental wave is defined as at least one of an acoustic        wave and electromagnetic wave; said elemental wave being at        least one of said peculiar shock-like wave and a forced wave;    -   (c) wave is defined as a complex wave being composed of        elemental waves, wherein said wave being characterized by        resulting amplitude defined as the vector sum of amplitudes of        said elemental waves;    -   (d) radiation jet-effect is defined as inter-related effects:        -   of a radiation pressure of wave, wherein the radiation            pressure is at least one of acoustic and electromagnetic,            and        -   of wave energy traveling in a prevalent direction, wherein            the wave energy is at least one of acoustic and            electromagnetic;    -   (e) acoustic waving jet-effect is defined as a kind of the        Coanda-jet-effect, being applied to inner portions of fluid, as        a tendency of an oscillatory moving-small-portion to be        attracted to and aligned with a curvature of a nearby fragment        of an imaginary boundary of said inner portion;    -   (f) electromagnetic waving jet-effect is defined as a tendency        of an electric field to be attracted to and aligned with a        nearby surface interacting with the electric field, wherein said        nearby surface is at least one of a real conductive wall and an        imaginary wall formed by force-lines of the electric field        itself;    -   (g) waving jet-effect is defined as at least one of the acoustic        waving jet-effect and the electromagnetic waving jet-effect;    -   (h) phobic-repulsing jet-effect is defined as a kind of        jet-effect, occurring in a fluid near to a surface made from a        fluid-repellent material;    -   (i) generalized jet-effect is defined as an effect of fluid        portion convective acceleration at the expense of fluid portion        internal heat energy that is inherently characterized by a        decrease in original temperature of said fluid portion in an        adiabatic process, wherein the generalized jet-effect is at        least one of the Venturi effect, the Coanda-jet-effect, the        acoustic waving jet-effect, the electromagnetic waving        jet-effect, the radiation jet-effect, and the phobic-repulsing        jet-effect;    -   (j) a usable wave power is defined as a partial wave power of a        complex wave being composed of elemental waves, being superposed        and thereby resulting in partially constructive interference and        partially destructive interference, wherein said partial wave        power being proportional to the second power of the resulting        amplitude of said wave, and hence being detectable by a classic        detector of waves, reacting on the resulting amplitude of wave;    -   (k) a latent wave power is defined as a partial wave power of a        complex wave being composed of elemental waves, being superposed        and thereby resulting in partially constructive interference and        partially destructive interference, wherein said partial wave        power being undetectable by a classic detector of waves,        reacting on the resulting amplitude of wave, and being        detectable by a thermal detector, reacting on the local thermal        radiation;    -   (l) warmth of a molecular fluid is defined as a storage of the        kinetic power of the fluid molecules;    -   (m) the universe background energy is defined as a latent energy        stored in space, wherein the universe background energy being        composed of at least the latent electromagnetic energy;    -   (n) fluid flow is defined as a molecular fluid, bringing the        warmth and origin kinetic power of motion in a prevalent        direction;    -   (o) the specific M-velocity, indicated by M*, related to said        fluid flow, is defined as equal to √{square root over        ((γ−1)/γ)}, where γ is so-called adiabatic compressibility        parameter of said molecular fluid;    -   (p) the specific kinetic power, indicated by W*, is defined as        kinetic power of fluid flow moving with the specific M-velocity        M*;    -   (q) a raw power is defined as a power yet to be in a useful        form;    -   (r) a generalized stock of said raw power is defined as at least        one of:        -   the warmth of ambient fluid, storing the kinetic power of            molecules, and        -   the universe background energy, storing the latent            electromagnetic energy;    -   (s) a starter power, indicated by W_(external), is defined as at        least one of:        -   thermal power harvested from a burned fuel,        -   external electrical power,        -   kinetic power of fluid flow,        -   internal heat power of fluid flow, frequently called warmth            of ambient fluid, and        -   electromagnetic power brought by sunlight;    -   (t) a generalized trigger of jet-effect is defined as a        component of a system, said component being characterized by a        field, being spread in ambient fluid medium and thereby making        said system to be open from the thermodynamics point of view,        wherein said component is at least one of:        -   a fluid flow 5.41, to trigger at least one of the Venturi            effect, the Coanda-jet-effect, and the waving jet-effect;            wherein the mentioned field is a field of flow velocities;            wherein, looking ahead in view of the description of            subparagraph “Convergent-Divergent Jet-Nozzle” referring to            FIG. 6a of the invention, it will become evident to a person            studied the present invention that the relatively slow fluid            flow 5.41, which yet can be accelerated by the            Coanda-jet-effect, is characterized by M-velocity being            lower than the specific M-velocity, indicated by M*,            specified in equation (6.9);        -   a fluid-repellent surface (for instance, similar to outer            surface 577 of spiral 576 shown in FIG. 5i ), to trigger the            phobic-repulsing jet-effect, wherein the mentioned field is            a field of repulsing forces; and        -   an electromagnetic field, to trigger the electromagnetic            waving jet-effect;    -   (u) an airfoil convexity of a corpus exposed to said fluid flow        is defined as a convexity being “embraced” by two edges in the        direction of said fluid flow motion, namely:        -   by a rounded leading edge, upstream of said fluid flow            motion; and        -   by a sharp trailing end, downstream of said fluid flow            motion;    -    thereby, providing airfoil properties of said corpus and hence        providing that said airfoil convexity, when interacting with        said fluid flow portion, causing a conversion of a portion of        said fluid warmth into a portion of kinetic power acquired by        said fluid flow portion due to the Coanda-jet-effect in an        adiabatic process;    -   (v) a generalized elemental source launching an elemental usable        power portion of at least W₁ is defined as a device transforming        an elemental pre-usable power portion into said elemental usable        power portion of at least W₁; wherein said generalized elemental        source is at least one of:        -   a fluid flow portion moving nearby said airfoil convexity            (for instance, similar to outer surface 577 of spiral 576            shown in FIG. 5i ),        -   wherein said elemental pre-usable power portion is composed            of an original internal heat power of fluid flow and an            original kinetic power of fluid flow; and        -   wherein said elemental usable power portion, equal to at            least W₁, is specified as the kinetic power of fluid flow            composed of the original kinetic power of fluid flow and an            additional portion of kinetic power acquired in an adiabatic            process due to at least one of the Venturi effect and the            Coanda-jet-effect;        -   an antenna of acoustic waves, capable of a receiving said            elemental pre-usable power portion, equal to at least W₁ and            a launching an acoustic wave bringing said elemental usable            power portion of at least W₁;        -   an antenna of electromagnetic waves, capable of a receiving            said elemental pre-usable power portion, equal to at least            W₁ and a launching an electromagnetic wave bringing said            elemental usable power portion of at least W₁;    -   (w) a generalized elemental feeder is defined as an interface of        power between said generalized stock and said generalized        elemental source, wherein said interface consuming said starter        power W_(external) and being capable of conversion said raw        power, extracted from said generalized stock, into said        elemental pre-usable power portion and supplying the elemental        pre-usable power portion to said generalized elemental source        launching said elemental usable power portion of at least W₁,        wherein said generalized elemental feeder being at least one of:        -   a fluid flow portion 5.41 moving nearby said airfoil            convexity of a corpus (for instance, similar to outer            surface 577 of spiral 576 shown in FIG. 5i ) exposed to said            fluid flow 5.41;        -   thereby, causing that:            -   (i) a portion of origin kinetic power, indicated by W₀,                brought by said fluid flow portion yet to be subjected                to the Coanda-jet-effect, being lower than the specific                kinetic power W*, and coming to said airfoil convexity,                and            -   (ii) the kinetic power, indicated by δW₁, of said fluid                flow portion, acquired due to the Coanda-jet-effect in                an adiabatic process,        -   both constitute said elemental pre-usable power portion,            indicated by W₁=W₀+δW₁, remaining lower than the specific            kinetic power W, and being higher than W₀ at least by factor            F₁ to satisfy the condition: F₁W₀=W₁<W*;        -   a generalized engine providing powering an antenna of            acoustic waves by said elemental pre-usable power portion of            at least W₁; and        -   a generalized engine providing powering an antenna of            electromagnetic waves by said elemental pre-usable power            portion of at least W₁;    -   (x) a generalized jet-converter of power is defined as an        aggregation comprising a conductor 5.30 of traveling power and a        gathering of N said generalized elemental sources (marked by set        5.10 of numerals: 5.11, 5.12, 5.13, . . . , 5.1N) launching        corresponding N said elemental usable power portions (marked by        numerals 5.31, 5.32, 5.33, . . . , 5.3N), wherein said        aggregation (5.30 and 5.10) providing an operation of said N        generalized elemental sources 5.10 (5.11, 5.12, 5.13, . . . ,        5.1N) in unison, thereby making said generalized jet-converter        of power being capable of a transformation said raw power into        said useful power 5.40, wherein said transformation is        implemented using a multi-stage repeating of said generalized        jet-effect provided by said generalized trigger of jet-effect;        said aggregation is at least one of:        -   an aggregation of a conductor 5.30 of flow and N said            airfoil convexities, sequentially arranged to be exposed to            said fluid flow portion, moving along said conductor of flow            and coming to said N airfoil convexities and flowing around            said N airfoil convexities sequentially, thereby, said            aggregation providing a sequential multi-stage repeated            action of said N airfoil convexities on said fluid flow            portion resulting in a corresponding multi-stage repeating            of the Coanda-jet-effect operation applied to said            transformation of said raw power into said useful power,            indicated by W_(N), in the form of kinetic power of a            resulting jetstream; thus, while said useful power remaining            substantially lower than the specific kinetic power W*, said            useful power W_(N) 5.40 of said resulting jetstream is            higher than said portion of origin kinetic power, indicated            by W₀, brought by said fluid flow portion 5.41 yet to be            subjected to the Coanda-jet-effect, by the factor of at            least F₁ ^(N);        -   an aggregation of a waveguide 5.30 and N said antennas of            waves, specifically arranged and synchronized to launch N            in-phase waves, correspondingly, and thereby to provide            constructive interference of said N in-phase waves within            said waveguide, wherein each of said N waves bringing said            elemental usable power portion of at least W₁ thereby            providing that said constructive interference of N said            waves thereby subjected to the waving jet-effect, in-phase            reinforced repeatedly N times, thereby forming a resulting            wave bringing said useful power 5.40 in form of wave power            of at least W_(N) being higher than the elemental pre-usable            power portion W₁ by the factor of N²;        -   wherein, without loss of generality but for the sake of            concretization, the inter-synchronization of the N sources            5.11, 5.12, 5.13, . . . , 5.1N of waves 5.31, 5.32, 5.33, .            . . , 5.3N, correspondingly, is implemented applying certain            delays, for instance, using a certain intervals 5.42 between            the sources 5.11, 5.12, 5.13, . . . , 5.1N, thereby            providing for that, when propagating within waveguide 5.30,            the waves 5.31, 5.32, 5.33, . . . , 5.3N become in-phase            superposed thereby resulting in constructive interference;            and    -   (y) said generalized power converter 5.20 is defined as an        engine providing a mechanism for a reincarnation of said useful        power 5.40 into said useful-beneficial power, wherein said        engine is at least one of:        -   open space, thereby providing conditions for reincarnation            of said useful power W_(N) of said resulting jetstream into            said jet-thrust power, according to Newton's Third Law;        -   a turbo-generator (shown schematically as a generalized            antenna 5.20), capable of transformation said useful power            W_(N) of said resulting jetstream 5.40 into the electrical            power 5.42;        -   a Peltier element operating as a thermoelectric generator,            primary producing electricity from the temperature            difference caused by said generalized jet-effect;        -   a generalized receiving antenna 5.20 having a feeder output            5.42, wherein said generalized receiving antenna 5.20 being            capable of conversion said useful power W_(N) 5.40 of said            resulting wave 5.40 into the electrical power 5.42, and            wherein said feeder output 5.42 providing the electrical            power release.            The generalized generator 5.00 comprises the following            generalized constituent elements:    -   a generalized starter, being composed of:        -   said ambient fluid medium;        -   N generalized elemental feeders, enumerated by 5.21, 5.22,            5.23, . . . , 5.2N, being energetically inter-independently            powered; and        -   a generalized stock of a raw power, storing the power yet to            be in a useful form;    -   a generalized trigger of the generalized jet-effect; and    -   a generalized jet-converter of power, comprising an aggregation        of a conductor 5.30 of traveling power and a gathering 5.10 of N        generalized elemental sources, enumerated by 5.11, 5.12, 5.13, .        . . , 5.1N, launching N elemental usable power portions,        enumerated by 5.31, 5.32, 5.33, . . . , 5.3N, correspondingly;        wherein the triple-dots, having numerals 5.14 and 5.24:        -   symbolize the conformance between the N generalized            energetically inter-independent feeders and the N            generalized elemental sources of the N elemental usable            power portions correspondingly, as well as        -   say that, preferably, N is a certain big number, wherein the            big integer number N having the claimed sense is at least            10;    -   and    -   a generalized power converter 5.20 transforming said useful        power into said useful-beneficial power.

In relation to electromagnetic waves, without loss of generality but forthe sake of concretization only, the waveguide 5.30 is characterized bya high dielectric constant, higher than the dielectric constant of theambient medium, wherein the high dielectric constant provides for thecondition of the so-called total internal reflection of theelectromagnetic waves, i.e. providing for a hypothetically ideallossless waveguide effect.

In relation to both: the acoustic waves and the electromagnetic waves,each of the N sources 5.11, 5.12, 5.13, . . . , 5.1N of waves 5.31,5.32, 5.33, . . . , 5.3N, correspondingly, consumes the power W₀ andlaunches a wave (one of 5.31, 5.32, 5.33, . . . , 5.3N, correspondingly)bringing the wave power W₁. Speaking strictly, as it follows from thedescription expound hereinabove in subparagraphs “Interference ofAcoustic Waves” and “Hypothetic Electromagnetic Analogue”, the consumedpower W₀ differs from the wave power W₁ brought by the wave, wherein thedifference (W₁−W₀), on the one hand, is defined by a positive powerportion acquired due to the waving jet-effect and radiation jet-effectand, on the other hand, is defined also by a negative power portion lostdue to wave power dissipation in the ambient medium. When ignoring thenegative power portion, one usually interprets that W₁=W₀, just ignoringthe work for the wave energy travelling itself that must be supported bya certain power according to The Energy Conservation Law. The mentionedpositive power portion, harvested due to the waving jet-effect, goes forthe wave energy travelling. Normally, the consideration of the wavepower without the power consumption for the wave energy traveling itselfis justified when one estimates a useful-beneficial power only.

The inventor emphasizes that sources 5.11, 5.12, 5.13, . . . , 5.1N ofwaves 5.31, 5.32, 5.33, . . . , 5.3N, correspondingly, are fedenergetically inter-independently. For example, each of the sourcesconsumes the power from a separate generalized generator of electricalsignals to feed the corresponding wave. Alternatively, a feeding, usingdifferent periods of a wave, is also interpreted as energeticallyinter-independent; but in contrast, a “multi-source” feeding,implemented by means of a splitting of a high power, cannot beinterpreted as an inter-independent feeding.

The inventor points out that the importance of the energeticinter-independence of the sources 5.11, 5.12, 5.13, . . . , 5.1N ispredetermined by the reciprocity theorem, which, when applied to thecase, saying that, when a parent wave, bringing the usable wave energyU_(N) per wavelength, is subjected to a decomposition thereby forming Ncoherent daughter waves, each daughter wave brings the usable waveenergy U₁ per wavelength that is lower than the parent usable waveenergy U_(N) per wavelength by the factor N², but not by the factor N,wherein the lack of the wave energy, equal to ΔU_(N)=N(N−1)U₁, becomestransformed into the latent energy of the ambient medium (in the case ofelectromagnetic waves, the ambient medium is the vacuum filled by theuniverse background energy, comprising the latent energy of“electromagnetic gas”).

Thus, considering actually energetically inter-independent sources 5.11,5.12, 5.13, . . . , 5.1N, for the sake of simplicity, ignoring thedifference between W₀ and W₁, the sum power W_(N1), consumed by the Nenergetically inter-independently fed sources 5.11, 5.12, 5.13, . . . ,5.1N, is equal to W_(N1)=NW₁. The inter-synchronization of the N sources5.11, 5.12, 5.13, . . . , 5.1N of waves 5.31, 5.32, 5.33, . . . , 5.3Nis implemented applying certain delays, for instance, using certainintervals 5.42 between the sources 5.11, 5.12, 5.13, . . . , 5.1N,thereby providing for that, when propagating within waveguide 5.30, thewaves 5.31, 5.32, 5.33, . . . , 5.3N become in-phase superposed therebyresulting in constructive interference.

The constructive interference is the resulting extra-high power wave5.40 characterized by the increased amplitude (for instance, theamplitude of oscillating electric field), wherein the amplitude increaseis specified by the factor N that corresponds to the resulting wavepower W_(N2) equal to W_(N2)=N²W₁=NW_(N1).

The inventor points out to the power difference between W_(N2) andW_(N1), namely, (W_(N2)−W_(N1))=N(N−1)W₁. In the case of acoustic waves,the power difference is acquired at the expense of the molecular fluidwarmth, and in the case of electromagnetic waves, the power differenceis acquired at the expense of the universe background energy (at leastat the expense of the latent electromagnetic energy stored in theelectromagnetic gas). Without loss of generality, the generalized powerconverter 5.20 is implemented as an antenna, exposed to the extra-highpower wave 5.40. Generalized power converter 5.20 is capable ofconversion of the extra-high power W_(N2) of wave 5.40 into theelectrical power released from feeder output 5.42 of generalizeddetector 5.20.

The inventor points out that, in contrast to the resonance electricalscheme of Tesla coil applied to induced oscillating electrical currentto enable a radiation of super-impressive lightning impulses, theproposed superposition of N in-phase electromagnetic waves (wherein N isa specified number), to provide for the desired constructiveinterference bringing usable wave power, is easily controllable.

Gravity-Jet Engine

FIG. 5m is a schematic illustration of motionless gravity-jet engines:5.50 and 5.60, each comprising an elaborated airfoil shaped container:gauge 5.51 and primary 5.61, correspondingly, being permanently filledwith liquid (for instance, water) 5.70 characterized by the density,substantially higher than the density of ambient gas (for instance,air). The upper surface of water in each of containers: 5.51 and 5.61,is on level 5.71 and has cross-sectional area A₀ 5.72. The inner side ofthe container walls is hydrophobic (to reduce the walls resistance) andthe elaborated airfoil shape of each of containers: 5.51 and 5.61,provides the condition of a cross-sectional area decrease in thevertical direction from the value A₀ 5.72 to the value A₁ 5.73 that (thedecrease) corresponds to the cross-sectional area decrease for water,which is freely falling in the gravitational field.

The inventor points out that the freely falling of fluid occurs with anacceleration, which differs from the gravitational acceleration of amaterial point (or sold body) by an additionally acquired acceleration,because of two accompanying effects, namely:

-   -   a part of potential energy goes for a work for deformation of        the falling fluid portions, which (the deformation) results in        elongation of water portions in the vertical direction, i.e.        results in the acquired acceleration by definition, and, in        turn,    -   the fluid portions deformation in combination with the fluid        motion is inevitably accompanied by the Venturi effect having        the jet-effect nature, thereby providing for the additionally        acquired acceleration at the expense of the internal heat of the        fluid.

The gauge container 5.51 is supplied with gauge curvedconvergent-divergent nozzle 5.52 and the primary container 5.61 issupplied with primary curved converging nozzle 5.62, wherein the volumeof the container (5.51 or 5.61) is much bigger than the volume of nozzle(5.52 or 5.62, correspondingly) to ignore of the moving water pulsechange when considering the water stream changing the velocity vectorwithin the curved nozzle (5.52 or 5.62, correspondingly). Wherein:

-   -   The gauge convergent-divergent nozzle 5.52 is beginning from        cross-section 5.73 and leading to gauge-ending cross-section        5.53, wherein the beginning and ending cross-sections: 5.73 and        5.53, correspondingly, both have identical area equal to A₁ and        both are located at the same level 5.74, which is lower than        level 5.71 on height h₀ 5.75; and moreover, the varying        cross-section of the convergent part is adapted to freely        descending water and the divergent part is aligned inversely to        the convergent part (i.e. adapted to freely ascending and        retarding water); and    -   The primary converging nozzle 5.62 having an elaborated airfoil        cross-section beginning from cross-section 5.73 and leading to        primary-ending cross-section 5.63, wherein the both        cross-sections are at the same level 5.74 such that the distance        between levels 5.71 and 5.74 equals h₀ 5.75; and wherein the        area A₁ of beginning cross-section 5.73 is greater than the area        A₂ of primary-ending cross-section 5.63 by the factor F of        constriction, i.e. A₁=F×A₂ A₁=F×A₂. Looking ahead, the equations        (6.13) and (6.14), described hereinbelow in subparagraph        “Convergent-Divergent Jet-Nozzle” with reference to FIG. 6a ,        when applied to a fluid flowing through an elaborated        actually-airfoil convergent-divergent jet-nozzle with extremely        low M-velocities, is applicable to a proper design of the        mentioned elaborated airfoil converging nozzle 5.62 to provide        for the water stream laminarity when the water stream is        subjected to the Venturi effect. This means that to implement        the constriction factor, for instance, F=2, and, at the same        time, to provide for the laminarity of fluid flowing through the        converging nozzle, one has to apply equation (6.14) to provide        for the desired linear (or at least substantially gradual)        change of the fluid static pressure.

The water, which is located in each of elaborated airfoil shapedcontainers 5.51 and 5.61 above level 5.74, performs a gravity compressor(with respect to nozzles 5.52 and 5.62, correspondingly) operating inthe gravitational field having force-lines in the vertical direction.

The gauge nozzle 5.52 and the primary nozzle 5.62, both provide for anoutflowing water jetstream, moving through the ambient air in thegravitational field and associated with trajectory: gauge 5.55 andprimary 5.65, correspondingly.

Ignoring the dragging effects acting by ambient air on a water jetstreamas well as ignoring the mentioned additionally acquired acceleration dueto the accompanying Venturi effect, the trajectory of water jetstream:either gauge 5.52 or primary 5.62, is described by parabola expressedwith respect to butt-end point: either 5.56 or 5.66, correspondingly,as:

$\begin{matrix}{{y = {{t\;{{\mathcal{g}}(\theta)} \times x} - {\frac{\mathcal{g}}{2u^{2}\cos^{2}\theta}x^{2}}}},} & {{Eq}.\mspace{14mu}\left( {5.11a} \right)}\end{matrix}$where x and y are coordinates in the horizontal and vertical directions,correspondingly, θ is angle (either 5.57 or 5.67) between the vectorvelocity of jetstream associated with trajectory (either 5.55 or 5.65,correspondingly) at butt-end point (either 5.56 or 5.66,correspondingly) and a horizontal axis, g is gravitational acceleration,and u is the absolute velocity: either u₁ or u₂, of headway motion ofthe outflowing jetstream associated with trajectory: either 5.55 or5.65, correspondingly, at butt-end point: either 5.56 or 5.66,correspondingly.

The absolute velocity u is determined by the height h₀ 5.75 andexpressed by:u=(1−ψ)√{square root over (Ψ2gh ₀)}  Eq. (5.11b),according to Torricelli's law, where the factors Ψ and ψ are introduced,wherein:

-   -   the introduced factor of effective acceleration increase Ψ        characterizes the mentioned interrelated effects: the        accompanying Venturi effect and a change in internal heat of the        unbrokenly and laminarly moving water with respect to the heat        of a water portion in container (5.51 or 5.61) near the surface        5.72, wherein the effective acceleration increase Ψ is averaged        over the height h₀ when the water motion is steady-state. The        deformation of the moving water portions shape results in a        change in the water portions thermodynamic state. In particular,        when the shape of a water portion becomes conic, the absolute        velocity u has two orthogonal components: of a headway motion        u_(H) and of a cross-sectional collapsing u_(C), wherein the        condition u=√{square root over (u_(H) ²+u_(C) ²)} is satisfied.        The headway motion component u_(H) characterizes the water flow        Φ=ρu_(H), where ρ is the density of substantially incompressible        water, while the cross-sectional collapsing component u_(C)        characterizes a water portion acquired acceleration, wherein the        acquired acceleration occurs at the expense of either potential        energy stored in the gravitational field and/or internal heat        energy stored in the Brownian motion of fluid molecules. The        cross-sectional collapsing component u_(C) of freely falling        water, defined as u_(C)=0.5×dD/dt, where D is the effective        linear size of cross-section (for instance, the diameter of a        circle cross-section), is approximately estimated by:

$\begin{matrix}{{u_{c} \approx \frac{{\mathcal{g}}\sqrt{{Au}_{H}}}{4\sqrt{\pi}\sqrt[4]{u_{H}^{2} + {2{\mathcal{g}}\; h}}} \approx \frac{{\mathcal{g}}\sqrt{{Au}_{H}}}{4\sqrt{\pi}\sqrt[4]{2{\mathcal{g}}\;{h\left( {\Psi + 1} \right)}}}},} & {{Eq}.\mspace{14mu}\left( {5.11c} \right)}\end{matrix}$where A is the cross-sectional area at the height level h. The conditionΨ=1 is applicable, for instance, to a falling small drop or to water ina container having a uniform cross-section, where, hypothetically, thewater descends laminarly and forcibly without the cross-sectionalcollapsing and so without acceleration. The condition u_(C)>0 inevitablyinterrelates with the condition Ψ>1. The value of the effectiveacceleration increase factor Ψ is quantified hereinbelow in equations(5.11i) and (5.11k); and

-   -   the introduced factor of velocity reduction ψ (0≤ψ≤1)        characterizes loss of the water stream headway motion kinetic        energy due to the dragging effects and turbulence within        container (5.51 or 5.61) and nozzle (5.52 or 5.62). A        not-optimized shape of the container and nozzle results in the        turbulence, which, in turn, results in dividing the kinetic        energy of the water stream between the kinetic energy of headway        motion and the kinetic energy of turbulent motion. The        skin-friction between the moving water and nozzle, on the one        hand, results in a decrease of the kinetic energy of water        stream within the container and nozzle, and on the other hand,        contributes to the turbulence. When the accelerated motion of        water within the container is turbulent and the nozzle is        resistive for the water motion, the factor of velocity reduction        ψ becomes significant. Hypothetically ignoring the dragging        effects and the turbulence within the container and nozzle, the        factor of velocity reduction ψ equals zero.

The mentioned elaborated airfoil shape of the container (5.51 or 5.61)and the inner surface of walls being hydrophobic, altogether providethat the condition ψ=0 is satisfied between levels 5.71 and 5.74.

To define the effective acceleration increase factor Ψ, two fundamentallaws: the equation of continuity and the Bernoulli theorem (the energyconservation law), are applied to the unbrokenly falling water. Namely,the velocity values u_(0H) and u_(1H), where u_(0H) and u_(1H) are thecomponents of water headway (in the case, dominantly vertical) motionvelocities at cross-sections 5.72 and 5.73, correspondingly, areinterrelated by the equation of continuity, namely:A ₁ u _(1H) =A ₀ u _(0H)  Eq. (5.11d).The absolute velocities u₀ and u₁, both comprising also correspondingcross-sectional collapsing components, are interrelated by the Bernoullitheorem, for instance, written in the form of equation (5.10b), namely,

$\begin{matrix}{{{\frac{u_{0}^{2}}{2} + {{\mathcal{g}}\; h_{0}}} = {\frac{u_{1}^{2}}{2} + {R\;\Delta\; T}}},} & {{Eq}.\mspace{14mu}\left( {5.11e} \right)}\end{matrix}$where R is specific fluid constant, and ΔT is the change in the absolutetemperature of moving water that is determined by the cross-sectionalcollapsing component of the moving water velocity. Therefore,

$\quad\left\{ \begin{matrix}{\frac{u_{0C}^{2}}{2} = {\frac{u_{1C}^{2}}{2} + {R\;\Delta\; T}}} & {\mspace{365mu}{{Eq}.\mspace{14mu}\left( {5.11f} \right)}} \\{{\frac{u_{0H}^{2}}{2} + {{\mathcal{g}}\; h_{0}}} = \frac{u_{1H}^{2}}{2}} & {\mspace{365mu}{{Eq}.\mspace{14mu}\left( {5.11g} \right)}}\end{matrix} \right.$Combining equations (5.11d) and (5.11g), one obtains:

$\begin{matrix}{u_{1H}^{2} = {2{\mathcal{g}}\; h_{0}{\frac{A_{0}^{2}}{A_{0}^{2} - A_{1}^{2}}.}}} & {{Eq}.\mspace{14mu}\left( {5.11h} \right)}\end{matrix}$Comparing (5.11h) and Torricelli's law, written in the form of equation(5.11b), the effective acceleration increase factor Ψ on the height h₀is expressed by:

$\begin{matrix}{\Psi = {\left( \frac{A_{0}^{2}}{A_{0}^{2} - A_{1}^{2}} \right).}} & {{Eq}.\mspace{14mu}\left( {5.11i} \right)}\end{matrix}$The equation (5.11i) makes it evident that the effective accelerationincrease factor Ψ is greater than 1 for the case.The area A₁ of the cross-section 5.73, specified for freely fallingwater, related to the height h₀ and velocity u_(0H) at cross-section5.72, is expressed by:

$\begin{matrix}{A_{1} = {\frac{A_{0}\mspace{14mu} u_{0H}}{\sqrt{u_{0H}^{2} + {2\Psi\;{\mathcal{g}}\; h_{0}}}}.}} & {{Eq}.\mspace{14mu}\left( {5.11j} \right)}\end{matrix}$Using again the equation of continuity Eq. (5.11d) and the Bernoullitheorem Eq. (5.11g), and taking into account equation (511j) for thearea A₁ in equation (5.11i), the effective acceleration increase factorΨ is expressed via u_(0H) and h₀, namely,

$\begin{matrix}{\Psi = {\frac{1}{2} + {\sqrt{\frac{1}{4} + \frac{u_{0H}^{2}}{2{\mathcal{g}}\; h_{0}}}.}}} & {{Eq}.\mspace{14mu}\left( {5.11k} \right)}\end{matrix}$Thereby, the effective acceleration increase factor Ψ is estimated as:

$\Psi = \left\{ \begin{matrix}{{\Psi > 1},} & {{{{if}\mspace{14mu}{\mathcal{g}}\; h_{0}} > 0},} & {i.e.\mspace{14mu}{falling}} \\{{\Psi = 1},} & {{{{if}\mspace{14mu}{\mathcal{g}}\; h_{0}} = 0},} & {{i.e.\mspace{14mu} u_{0H}} = 0} \\{{0 < \Psi < 1},} & {{{{if}\mspace{14mu}{\mathcal{g}}\; h_{0}} < 0},} & {i.e.\mspace{14mu}{upping}}\end{matrix} \right.$The inventor points out that, based on two fundamental laws: theequation of continuity an the energy conservation (the Bernoullitheorem), both applied to the unbrokenly falling water, the summary thatthe water stream free falling with an acceleration higher than thegravitational acceleration g is one of the primary teachings of thepresent invention.

The absolute velocity of water moving through cross-section 5.73 isestimated as:

$\begin{matrix}{\mspace{76mu}{{{{{u_{1} = \sqrt{u_{1H}^{2} + u_{1C}^{2}}},\mspace{76mu}{where}}u_{1H}^{2}} = {{2\Psi\;{\mathcal{g}}\; h_{0}\mspace{14mu}{and}\mspace{14mu} u_{1C}^{2}} \approx {\frac{1}{16\pi}\frac{g^{2}\mspace{14mu} A_{0}u_{0H}}{\sqrt{2{\mathcal{g}}\;{h_{0}\left( {\Psi + 1} \right)}}}} \approx {\frac{1}{16\pi}\frac{g^{2}\mspace{14mu} A_{0}u_{0H}}{\sqrt{u_{H}^{2} + {2{\mathcal{g}}\; h}}}}}},}} & {{Eq}.\mspace{14mu}\left( {5.11l} \right)}\end{matrix}$

The shape of nozzle 5.52 has the varying cross-sectional area adapted tofreely descending and freely ascending water such that thermodynamicstates of water in positions 5.73 and 5.53 are identical. Thereby, thevelocity of water portion at position 5.56 is equal to u₁ specified byequation (5.11l). The maximal height h₁ 5.58 of the water jetstreamassociated with trajectory 5.55 is equal to h₁=(u_(1H) sin θ)²/(2Ψg),wherein when θ=60°, Ψ≈1, and ψ=0, then h₁=0.75h₀. The condition h₁<h₀ issatisfied.

In contrast to nozzle 5.52, nozzle 5.62 is asymmetrical, having the areaA₁ of cross-section 5.73 bigger than the area A₂ of primary-endingcross-section 5.63 by the factor F of constriction, i.e. A₁=F×A₂.

Nozzle 5.62 provides for the Venture effect (having the jet-effectnature) and so providing for a convective acceleration of the portionmoving through the nozzle such that velocity u₂ at point 5.66 becomeshigher than the velocity u₁ at position 5.73 by the factor F, i.e.u₂=F×u₁ in accordance with the equation of continuity, wherein thevelocity increase occurs at the expense of the water warmth.

The mentioned condition that the volume of container 5.61 is much biggerthan the volume of nozzle 5.62, justifies the assumption that thevelocity u₁ of water motion at the position 5.73 of both containers 5.51and 5.61 is the same.

The inventor points out that, in accordance with the Bernoulli theoremapplied to the water streaming through nozzle 5.62, the values u₁ and u₂are interrelated as:

$\frac{u_{1}^{2}}{2} = {\frac{u_{2}^{2}}{2} + {R\;\Delta\; T}}$where the negative value of the water absolute temperature change ΔTprovides for the contribution to the kinetic energy of the outflowingwater jet-stream.

The increased velocity u₂=F×u₁ corresponds to another parabolictrajectory of the water jetstream 5.62. If, hypothetically, ψ=0 and, forexample, angle 5.66 equals θ₂=60° and the factor of constriction equalsF=2, then the maximal height h₂ 5.68 of water jetstream 5.62 equalsh₂=F²h₁=3h₀.

The inventor points out that the condition h₂>h₀ becomes reachable whenthe Venturi effect is triggered keeping the water motion laminar.

It will be evident to a person skilled in the art that a use of theheight h₂ 5.68 of a waterfall for producing the electrical power using ahydro-turbine [not shown here] is more efficient than a use of theorigin height h₀ 5.75. Furthermore, the height difference (h₂−h₀) 5.76allows for the electricity harvesting and wherein reverting a fallingwater portion back into container 5.61 [not shown here] and therebyavoiding a consumption of the water from container 5.61. For such apermanent use of the water portion, the water must permanently beconsuming caloric, for instance, from ambient warmth. The inventorpoints out that this is not a so-called “Perpetuum mobile”, but a use ofwater heat and the heat of ambient air to produce useful power, stronglyaccording to the Energy Conservation Law.

The inventor points out that the described technique allowing for thetransformation of water warmth into useful energy is composed of twoobvious transformations:

-   -   a gravitational acceleration of water stream in the Earth        gravitational field; and    -   a convective acceleration of water jetstream using an elaborated        airfoil nozzle;        wherein the combination of the two obvious transformations        provides for a new quality of motionless gravity-jet engine        5.60. Namely, this allows for the harvesting of useful power        from the heat of water. The combination of a gravity compressor        and an elaborated airfoil converging (or convergent-divergent)        nozzle is one of the primary teachings of the present invention.

In view of the foregoing description referring to FIG. 5m , it will beevident for a person studied the present invention that:

-   -   motionless gravity-jet engine 5.60 launching water jetstream        5.65, as a waterfall, is applicable to a hydro-turbine; wherein,        the motionless gravity-jet engine, when operating in a mode        reverting water portions back into container 5.62 and if the        falling water is further powers the hydro-turbine (which, in the        final analysis, producing electrical power at the expense of the        water warmth), at the same time, allows for cooling the water        almost reaching the freezing point;    -   motionless gravity-jet engine 5.60 can be cascaded multi-stage        repeatedly (implementing a hydro-gateway) to increase the        cumulative height of waterfall; and, looking ahead,    -   the equation (6.14), mentioned hereinabove and described        hereinbelow in subparagraph “Convergent-Divergent Jet-Nozzle”        with reference to FIG. 6a , in particular, assuming Venturi        M-velocities (where the term “Venturi M-velocity” will be        introduced), is applicable to design an elaborated shape of        airfoil container 5.61, to provide an additionally acquired        acceleration and laminarity of water motion.        Convergent-Divergent Jet-Nozzle

FIG. 6a is a schematic illustration of a convergent-divergent jet-nozzle610, pipe-section in a sagittal plane. Convergent-divergent jet-nozzle610 is applied to accelerate a compressed and hot air stream, or moregenerally, a laminarly flowing compressed and hotcompressible-expandable fluid 611. Convergent-divergent jet-nozzle 610has the inner tunnel opposite walls shaped, for simplicity,axis-symmetrically around an imaginary sagittal x-axis 615, as aconvergent funnel 612 having open inlet, narrow throat 613 comprisingpoint 618 of the narrowest cross-section, and divergent exhaust tailpipe614 having open outlet, constructed according to an exemplary embodimentof the present invention providing the improved de Laval jet-effect. Forsimplicity, compressed and hot fluid stream 611 has a uniform front atthe inlet.

For the purposes of the present patent application, the de Laval effectshould be understood in a wide sense as comprising both: the de Lavaljet-effect, defined as an effect of flow extra-acceleration, and the deLaval retarding-effect, defined as an effect of flow extra-slowing.Thus, the de Laval jet-effect is a particular case of the de Lavaleffect.

The specifically shaped tunnel, comprising the three major successiveconstituents: convergent funnel 612 having an open inlet, narrow throat613, and divergent exhaust tailpipe 614 having an open outlet, has noreal separation features between the constituents. For the purpose ofthe present patent application, narrow throat 613 is specified as afragment of the inner tunnel located between imaginary inlet 6131 andoutlet 6132. For the purposes of the present patent application, theterm “principal interval” of the x-axis is introduced as correspondingto the interval occupied by the specifically shaped tunnel, i.e. atleast comprising narrow throat 613.

Fluid stream 611 is subjected to the Coanda-effect, observed as aligningof fluid stream 611 with the curvature of specifically shaped walls ofthe inner tunnel. The Coanda-effect is defined by a non-zero partialpressure-“c” P_(c) arising when the shape of a fluid portion is varyingas the fluid portion moves along the shaped inner tunnel ofconvergent-divergent jet-nozzle 610. Looking ahead, point out that thespecific shape of tunnel, constructed according to the principles of thepresent invention, prevents disturbances of the fluid motion. Thisstipulation corresponds to the case when thecumulative-inner-static-pressure P of streaming fluid 611 is varyinggradually and the velocity of streaming fluid 611 is varying linearly asthe fluid 611 moves within the shaped tunnel along imaginary sagittalx-axis 615.

For simplicity, imaginary sagittal x-axis 615 is horizontal, i.e. movingfluid 611 does not change its effective height above the Earth's oceansurface level. Thus, equations (5.6) and (5.7) for a stationary laminarflow can be written as (6.1) and (6.2) correspondingly:udu+dQ=0  Eq. (6.1),uρA=C=Const  Eq. (6.2),where C is a constant associated with the considered fluid portion, andvalues A, u, and ρ are associated with the flow cross-section: A is theflow cross-section area, u is the flow velocity, and ρ is the fluiddensity. Introduce value of volume of unit mass v, defined as v=1/ρ.

The fluid characteristic heat portion per unit mass is defined asQ=P/ρ=Pv, so dQ=vdP+Pdv, where P=P_(in)=P_(s)+P_(drag)+P_(viscous).Therefore, equation (6.1) can be represented asudu+vdP+pdv=0  Eq. (6.3a).Dividing (6.3a) by Pv, one obtains:

$\begin{matrix}{{{\frac{udu}{Pv} + \frac{dP}{P} + \frac{dv}{v}} = 0},} & {{Eq}.\mspace{14mu}\left( {6.3b} \right)}\end{matrix}$and so,

$\begin{matrix}{\frac{dv}{v} = {{- \frac{udu}{Pv}} - {\frac{dP}{P}.}}} & {{Eq}.\mspace{14mu}(6.3)}\end{matrix}$Rewrite equation (6.2) as:uA=Cv  Eq. (6.4a).and further in differential form as:Adu+udA=Cdv  Eq. (6.4b).Divide the left and right sides of (6.4b) by the left and right sides of(6.4a) correspondingly:

$\begin{matrix}{{\frac{du}{u} + \frac{dA}{A}} = {\frac{dv}{v}.}} & {{Eq}.\mspace{14mu}(6.4)}\end{matrix}$Referring to equation (5.8a) for a real molecular fluid undergoing areversible adiabatic process, one can write: Pv^(γ)=Const, or indifferential form:v ^(γ) dP+γPv ^(γ-1) dv=0  Eq. (6.5a).Dividing (6.5a) by γPv^(γ), one obtains:

$\begin{matrix}{\frac{dv}{v} = {+ {\frac{dP}{\gamma\; P}.}}} & {{Eq}.\mspace{14mu}(6.5)}\end{matrix}$Comparing (6.5) and (6.3), one can write:

$\begin{matrix}{{{{- \frac{udu}{Pv}} - \frac{dP}{P}} = {- \frac{dP}{\gamma\; P}}},{i.e.}} & {{Eq}.\mspace{14mu}\left( {6.6a} \right)} \\{{{- \frac{udu}{Pv}}\frac{\gamma\; u}{\gamma\; u}} = {{- \frac{dP}{\gamma\; P}} + {\frac{\gamma}{\gamma}{\frac{dP}{P}.}}}} & {{Eq}.\mspace{14mu}\left( {6.6b} \right)}\end{matrix}$The denominator of the left side of (6.6b) comprises value (γPv) thatdefines velocity of sound via equation u_(sound)=√{square root over(γPv)}, so (6.6b) can be rewritten as:

$\begin{matrix}{{{- \frac{\gamma\; u^{2}}{u_{sound}^{2}}}\frac{du}{u}} = {\frac{\gamma - 1}{\gamma}{\frac{dP}{P}.}}} & {{Eq}.\mspace{14mu}\left( {6.6c} \right)}\end{matrix}$Introducing the value M=u/u_(sound) having the meaning of the fluidportion velocity measured in Mach numbers, i.e. M-velocity, (6.6c) canbe written as:

$\begin{matrix}{{{- \gamma}\; M^{2}\frac{du}{u}} = {\frac{\left( {\gamma - 1} \right)}{\gamma}{\frac{dP}{P}.}}} & {{Eq}.\mspace{14mu}(6.6)}\end{matrix}$Now comparing (6.5) and (6.4), one gets:

$\begin{matrix}{\frac{dP}{\gamma\; P} = {{- \frac{dA}{A}} - {\frac{du}{u}.}}} & {{Eq}.\mspace{14mu}(6.7)}\end{matrix}$Substituting the expression for dP/γP from (6.7) into (6.6), oneobtains:

${{- \gamma}\; M^{2}\frac{du}{u}} = {\left( {\gamma - 1} \right)\left( {{- \frac{dA}{A}} - \frac{du}{u}} \right)}$and after simple algebraic transformations one formulates:

$\begin{matrix}{\frac{dA}{A} = {\left( {{\frac{\gamma}{\gamma - 1}M^{2}} - 1} \right){\frac{du}{u}.}}} & {{Eq}.\mspace{14mu}(6.8)}\end{matrix}$Equation (6.8) comprises the term M²γ/(γ−1) characterizing the effect ofthe gas compressibility and expandability. Equation (6.8) differs fromclassical equation (1b) derived from the Euler equations applied to anideal fluid defined in frames of the continuum mechanics. In particular,equation (6.8) says that: if the horizontally moving flow is relativelyslow (i.e. M<√{square root over ((γ−1)/γ))}, then the narrowing of theflow cross-section (i.e. negative dA) corresponds to acceleration of theflow (i.e. positive du); and if the flow is relatively fast (i.e.M>√{square root over ((γ−1)/γ))}, then just the widening of the flowcross-section (i.e. positive dA) corresponds to acceleration of the flow(i.e. positive du). This means, in particular, that at so-called“critical condition” point 680 defined for the narrowest throat of thede Laval nozzle, the flow specific M-velocity equalsM*=√{square root over ((γ−1)/γ)}  Eq. (6.9).

For the purposes of the present patent application, here and further,the lower index “*” is applied to an M-velocity, geometrical andthermodynamic parameters in a critical condition point.

For air as a diatomic molecular gas, the generalized adiabaticcompressibility parameter γ equals γ=7/5=1.4, and M*=√{square root over((γ−1)/γ)}≈0.5345 Mach, but not 1 Mach as follows from classicalequation (1b). For a gas composed of multi-atomic molecules, thegeneralized adiabatic compressibility parameter γ is closer to 1, and sothe de Laval jet-effect is expected at lower M-velocities. In aparticular case of an almost incompressible liquid, the generalizedadiabatic compressibility parameter γ is extremely great and equation(6.8) comes close to classical equation (1b), for which M*=1 Mach.

In many actual and imaginary applications the phenomenon of shocksound-wave emission, that arises at M-velocities near 1 Mach, isundesirable or unacceptable. Therefore, the conclusion of resultingequation (6.8), that the de Laval jet-effect begins from the velocitybeing substantially lower than the speed of sound, becomes important toprovide for a utilization of this useful effect avoiding the phenomenonof shock sound-wave emission.

Now consider the case where a compressed and/or heated gas, defined bythe stagnation parameters: pressure P₀, density ρ₀, and temperature T₀,is launching into a convergent-divergent jet-nozzle. Let the stagnationpressure P₀, temperature T₀, and density ρ₀ be much high to provide thespecific M-velocity M*=√{square root over ((γ−1)/γ)} at the narrowestcross-section of the throat. The gas characteristic heat portion perunit mass, expressed in terms of the gas temperature, is: Q=RT.Substitution of this expression into (6.1) gives:

$\begin{matrix}{T_{0} = {{T + \frac{u^{2}}{2R}} = {T\left( {1 + {M^{2}\frac{\gamma}{2}}} \right)}}} & {{Eq}.\mspace{14mu}(6.10)}\end{matrix}$where T₀ is the stagnation temperature; T is the gas portion currenttemperature; u_(sound)=√{square root over (γPv)}=√{square root over(γRT)}, and M=u/u_(sound)=u/√{square root over (γRT)}. Though thenormalized value M depends on temperature, one retains the form ofequation (6.10) expressed via M, because the value of M=1 Mach has thephysical sense of the shock sound-wave emission condition. Taking intoaccount relations between thermodynamic parameters in an adiabaticprocess, equation (6.10) can be rewritten as:

$\begin{matrix}{\frac{T_{0}}{T} = {\left( \frac{P_{0}}{P} \right)^{\frac{\gamma - 1}{\gamma}} = {\left( \frac{\rho_{0}}{\rho} \right)^{\gamma - 1} = {1 + {M^{2}\frac{\gamma}{2}}}}}} & {{Eq}.\mspace{14mu}(6.11)}\end{matrix}$where P and ρ are the current static pressure and densitycorrespondingly.

It is important to introduce the ratio A/A*, where A* is the narrowestcross-sectional area of the nozzle throat, i.e. is the criticalcondition area corresponding to the critical condition point, and A isthe current cross-sectional area. It follows from (6.2) that

$\begin{matrix}{\frac{A}{A_{*}} = {\frac{\rho_{*}}{\rho}\frac{u_{*}}{u}}} & {{Eq}.\mspace{14mu}(6.12)}\end{matrix}$Taking into account (6.11) and that the specific M-velocity equalsM*=√{square root over ((γ−1)/γ)}, the ratio A/A* can be expressed viaM-velocity:

$\begin{matrix}{\frac{A}{A_{*}} = {\frac{1}{M}\left( \frac{\gamma - 1}{\gamma} \right)^{\frac{1}{2}}\left( \frac{2 + {\gamma\; M^{2}}}{\gamma + 1} \right)^{\frac{\gamma + 1}{2{({\gamma - 1})}}}}} & {{Eq}.\mspace{14mu}(6.13)}\end{matrix}$

Equation (6.13) is the equation of principle, bonding the generalizedadiabatic compressibility parameter γ, M-velocity M, and ratio A/A* ofthe molecular fluid, fast and laminarly flowing through the de Lavalnozzle, oriented horizontally. Equation (6.13) differs from classicalequation (1) derived basing on the Euler equations applied to an idealfluid defined in frames of the continuum mechanics. Equation (6.13), asone of the primary teachings of the present invention, says that toaccelerate a warmed and compressed air portion up to 1 Mach, one mustapply a convergent-divergent jet-nozzle and provide the nozzle innertunnel divergent part expansion up to the ratio of A/A*≈1.5197.Considering an essential M-velocity range, specified as an M-velocityrange comprising M-velocities corresponding to the flow passing throughthe principal interval, equation (6.13) can be applied to make an idealshape of the nozzle to provide for a laminar motion and thereby optimizethe acceleration of the streaming fluid at least in the essentialM-velocity range, i.e. at least within the specifically shaped tunnel.In contrast to the prior art concept of rapid expansion and accelerationof the gas, described hereinbefore with reference to FIGS. 1c and 1d ,that causes the arising of undesired Mach waves, the substantiallygradual (or linear) increase of the M-velocity downstream along the gasmotion accompanied by the interrelated gradual (or linear) change offluid thermodynamic parameters, is a criterion of the nozzle innertunnel shape optimization preventing turbulences and, in particular,providing suppression of the undesired Mach waves, according to anexemplary embodiment of the present invention.

Further, for the purposes of the present patent application, a use ofthe equation of principle (6.13) assumes an inherent condition of agradual change of the fluid thermodynamic parameters. So,axis-symmetrical convergent-divergent jet-nozzle 610, comprisingspecifically shaped convergent funnel 612 having an open inlet, narrowthroat 613, and divergent exhaust tailpipe 614 having an open outlet, isdesigned according to equation (6.13), where the value M corresponds tox-coordinates along imaginary x-axis 615 as a smooth function M(x). Inparticular, a linear function M(x) was chosen as a desired for M(x),i.e.

M(x)=M(x)=M*+α_(M)(x−x*), where x is the x-coordinate at x-axis 615, andα_(M) is a positive constant defining a scale factor and having a senseof constant gradient of M-velocity spatial distribution, i.e.α_(M)=∂M(x)/∂x. Such a relationship enables a substantially smoothedincrease of M-velocity as the fluid moves through the specificallyshaped tunnel of convergent-divergent jet-nozzle 610. The linearincrease of M-velocity prevents substantially the arising of streamingfluid 611 motion disturbances, accompanied by shock waves.

In contrast to a jump-like sharp slope, the gradual change of theM-velocity and so of all the interrelated thermodynamic parameters isone of the primary features of the de Laval jet-effect improvement.

For the purposes of the present patent application, the term “de Lavalenhanced jet-effect” or briefly: “enhanced jet-effect” is introduced asrelating to the modified de Laval jet-effect, occurring in aconvergent-divergent tunnel having a specifically revised shapeaccording to the principles of the present invention, such that themodified de Laval jet-effect becomes improved by smoothing of the fluidthermodynamic parameters spatial distribution, providing the followingbeneficial features:

-   -   smoothing of the flowing fluid M-velocity, providing suppression        of the undesired flow disturbances accompanied by shock waves;    -   smoothing of the flowing fluid static pressure, providing        suppression of the undesired Mach waves and, thereby,        suppression of nearby body vibrations;    -   smoothing of the flowing fluid temperature, providing        suppression of adjacent surface tensions; and    -   smoothing of the flowing fluid density, providing suppression of        shock waves.        Also, the term “de Laval-like jet-effect” should be understood        in a wider, sense including a case when an enhanced jet-effect        occurs in an open space imaginarily bordered by the flow        streamlines, wherein the imaginary borders constitute a        convergent-divergent shape, i.e. similar to a de Laval nozzle.

If the exhaust tailpipe 614's outlet area is A_(e), the ratio A_(e)/A*defines the nozzle expansion ratio that can be optimized in accordancewith the estimations described hereinbelow with reference to FIGS. 7a,7b , 7 c.

Thereby, a convergent-divergent jet-nozzle, constructed applyingequation (6.13) according to an exemplary embodiment of the presentinvention, allows a use of the de Laval enhanced jet-effect toaccelerate incoming compressed and hot airstream 611 moving with lowM-velocities to obtain outflowing accelerated and cooled jetstream 616,reaching high M-velocities [i.e. M-velocities, higher than the specificM-velocity M*=√{square root over ((γ−1)/γ)}], in particular,high-subsonic velocities.

FIG. 6b , in conjunction with FIG. 6a , is a schematic graphicillustration of the distribution of the flowing fluid 611's threeparameters: velocity 620, static pressure 630, and temperature 640 alongthe length of nozzle 610, constructed according to the principles of apreferred embodiment of the present invention. The narrowestcross-section of the throat 613 (FIG. 6a ) provides the “criticalcondition” point 618. Compressed and hot fluid 611 flows through throat613, where the velocity picks up 621 such that M-velocity reaches thespecific M-velocity M*=√{square root over ((γ−1)/γ)} 623 at the criticalcondition point 618. Ahead of the critical condition point 618, thepressure and temperature fall, correspondingly 631 and 641. Hot flowingfluid 611 crosses the critical condition point 618 and enters thewidening stage of throat 613 and further divergent exhaust tailpipe 614having an open outlet. Flowing fluid 611 expands there, and thisexpansion is optimized such that the extra-increase of M-velocity 622 issubstantially smoothed; and the pressure and temperature extra-decrease,632 and 642, correspondingly, are substantially smoothed as well, incontrast to that at the critical condition point 180 with reference tothe classic prior art rocket nozzle 100 of FIGS. 1c, 1d . The smoothedchange of static pressure 630 provides a suppression of unwanted Machwaves. In practice, the suppression of Mach waves provides a suppressionof undesired vibrations that, in particular, especially important forfast accelerating vehicles.

In view of the foregoing description referring to FIG. 6a , it will beevident to a person skilled in the art that one can use differentcriteria of a gradualness of M(x) for different preferred optimizationsof the convergent-divergent shape of a tunnel. Namely, the conditions,providing laminarity of the airstream motion, are:

-   -   if suppression of Mach waves and of body vibrations are the most        preferable, then M(x) should be given as the function

${{M(x)} = \sqrt{2\left\{ {\left\lbrack {P_{0}\text{/}{\overset{\_}{P}(x)}} \right\rbrack^{{({\gamma - 1})}\text{/}\gamma} - 1} \right\}\text{/}\gamma}},$

-   -    where P(x) is a linear function of the static pressure vs.        x-coordinate: P(x)=P*+α_(P)(x−x*), P* is the static pressure of        the flowing fluid at the critical condition point x*, and        α_(P)=∂P(x)/∂x is a constant gradient of the static pressure        distributed along the x-axis within a specially shaped tunnel;        and FIG. 6c is a schematic illustration of an exemplary profile        of an optimized specifically shaped tunnel providing a linear        change of the flowing fluid static pressure corresponding to the        essential M-velocity range comprising M-velocities from 0.02 up        to 2 Mach;    -   if the suppression of temperature jumps is the most preferable,        then M(x) should be given as the function

${{M(x)} = \sqrt{2\left\{ {\left\lbrack {T_{0}\text{/}{\overset{\_}{T}(x)}} \right\rbrack - 1} \right\}\text{/}\gamma}},$

-   -    where T(x) is a linear function of the fluid temperature vs.        x-coordinate: T(x)=T*+α_(t)(x−x*), T* is the temperature of the        flowing fluid at the critical condition point x*, and        α_(T)=∂T(x)/∂x is a constant gradient of the fluid temperature        distributed along the x-axis within a specially shaped tunnel;        and FIG. 6d is a schematic illustration of an exemplary profile        of an optimized specifically shaped tunnel providing a linear        change of the flowing fluid temperature corresponding to the        essential M-velocity range comprising M-velocities from 0.02 up        to 2 Mach; and    -   if a trade-off between suppressions of Mach waves and        temperature jumps is preferable, then M(x) should be given as        the function

${{M(x)} = \sqrt{2\left\{ {\left\lbrack {\rho_{0}\text{/}{\overset{\_}{\rho}(x)}} \right\rbrack^{({\gamma - 1})} - 1} \right\}\text{/}\gamma}},$

-   -    where ρ(x) is a linear function of the fluid density vs.        x-coordinate: ρ(x)=ρ*+α_(P)(x−x*), ρ* is the density of said        flowing fluid at the critical condition point x*, and        α_(ρ)=∂ρ(x)/∂x is a constant gradient of the fluid density        distributed along the x-axis within a specially shaped tunnel;        and FIG. 6e is a schematic illustration of an exemplary profile        of an optimized specifically shaped tunnel providing a linear        change of the flowing fluid density corresponding to the        essential M-velocity range comprising M-velocities from 0.02 up        to 2 Mach.

Further, for the purposes of the present invention, the term “airfoil”or “actually-airfoil” should be understood as related to a wall shapeand as specifying a convergent-divergent shape of a flow portion'sstreamlines aligned to the airfoil wall, wherein, in contrast to aseemingly-airfoil shape, the convergent-divergent shape calls for thedifferential equation of motion (6.8), equation of principle (6.13), andat least one of the aforementioned conditions for the function M(x),thereby providing laminarity of the flow portion motion.

Furthermore, it will be evident to a person skilled in the art that onecan optimize the specifically shaped tunnel of convergent-divergentjet-nozzle 610 providing such a conformity of the cross-sectional areaof the open inlet with the M-velocity of flowing fluid crossing the openinlet, that the flowing fluid M-velocity is substantially smooth at theentering the open inlet. Moreover, one can control the cross-sectionalarea of the open inlet, according to the equation of principle,providing conformity of the open inlet cross-sectional area with thevariable M-velocity of the entering flowing fluid afore-and-nearby theopen inlet. This may become important, for example, to suppressvibrations of a fast accelerating vehicle.

Moreover, it will be evident to a person skilled in the art that, assoon as the de Laval effect occurs in an adiabatic process, thecondition of fluid stream 611 motion through the narrowest cross-sectionof throat 613 at critical condition point 618 with the specificM-velocity M*=√{square root over ((γ−1)/γ)} 623, accompanied bythermodynamic parameters: static pressure P*, temperature T*, and fluiddensity ρ*, interrelates with a condition of fluid stream 611 motionwith an M-velocity and accompanied thermodynamic parameters staticpressure P, temperature T, and fluid density ρ at any cross-section ofconvergent-divergent jet-nozzle 610's inner tunnel, wherein theconditions interrelation depends on the tunnel geometry only. In otherwords, if a hypothetic propeller pushing a hypothetic inviscid fluidprovides the inviscid fluid laminar flow with the specific M-velocityM*=√{square root over ((γ−1)/γ)} at the critical condition point of a deLaval nozzle, then the de Laval effect becomes triggered in the de Lavalnozzle, wherein the thermodynamic parameters of the moving inviscidfluid portions are interrelated as in an adiabatic process. In thiscase, the hypothetic propeller triggering the de Laval effect expendspower for the launching of accompanying shock and/or Mach waves only.

In view of the foregoing description referring to FIG. 6a , it will beevident to a person skilled in the art that:

-   -   in a more general case, when imaginary sagittal axis 615 is        oriented at least partially in the vertical direction in the        Earth's gravitational field, the equation of principle should be        corrected becoming different from equation (6.13) by a component        depending on the gravitational acceleration g, namely:

$\begin{matrix}{{\frac{A}{A_{*}} = {\frac{M_{*}}{M}\left( \frac{1 + {\frac{\gamma}{2}M^{2}} + \frac{{\mathcal{g}\Delta}\; h}{RT}}{1 + {\frac{\gamma}{2}M_{*}^{2}}} \right)^{\frac{\gamma + 1}{2{({\gamma - 1})}}}}},} & {{Eq}.\mspace{14mu}(6.14)}\end{matrix}$

-   -   where Δh is a change of the flow effective height with respect        to the critical condition point. It will be further evident to a        person skilled in the art that, when the considered temperatures        and M-velocities are sufficiently high to provide for the        conditions: gΔh/RT<<1 and gΔh/RT<<γM²/2 to be satisfied, a use        of the equation of principle in the form of equation (6.13)        becomes justified;    -   taking into account molecular interactions for flowing liquid or        plasma, for which changes of the partial deep-stagnation        pressure-“a” δP_(a) become at least noticeably distributed in        space, the generalized adiabatic compressibility parameter γ in        the equation of principle (6.13) is not a constant, but varies        with the changes of the partial deep-stagnation pressure-“a”        δP_(a), in a conformance with equations (5.8b) and (5.8c);    -   if the flowing molecular fluid is an ionized gas, i.e. plasma,        controlled by an external magnetic field, then the specifically        shaped walls of tunnel can be imaginary, formed by streamlines        of the flowing plasma subjected to and controlled by an action        of the magnetic field; and    -   according to the kinetic theory of matter, a substantial        incompressible molecular fluid, characterized by almost not        changeable thermodynamic parameters: density, temperature, and        inner-static-pressure and characterized by the infinitely great        generalized adiabatic compressibility parameter γ→∞, cannot        change its cross-sectional area substantially, and so, according        to equation of principle (6.13), cannot flow laminarly through a        horizontal tunnel having a varying cross-sectional area; and        furthermore, strictly speaking, a hypothetical        absolutely-incompressible molecular fluid cannot flow through a        converging tunnel at all. This is a theoretically important        teaching of the present invention.        De Laval Retarding-Effect

FIG. 6f is a schematic illustration of an inverse convergent-divergentjet-nozzle 650, pipe-section in a sagittal plane. Convergent-divergentjet-nozzle 650, constructed according to the principles of a preferredembodiment of the present invention, as inverse de Laval nozzle, appliedto retard a fast fluid-flow 651, streaming with a high M-velocity M₆₅₁,higher than the specific M-velocity M*=√{square root over ((γ−1)/γ)}.Convergent-divergent jet-nozzle 650 has the sectional shapemirror-symmetrically congruent to the sectional shape ofconvergent-divergent jet-nozzle 610, shown in FIG. 6a , and oriented tooncoming fluid-flow 651 in the back direction. Namely, the shape isaxis-symmetrical around an imaginary sagittal axis 655; convergentfunnel 652 having open inlet is as inverse divergent exhaust tailpipe614; narrow throat 653 comprises point 658 of the narrowestcross-section; and divergent exhaust tailpipe 654 is as inverseconvergent funnel 612. Convergent funnel 652, narrow throat 653, anddivergent exhaust tailpipe 654 have not real separation features betweenthem. For the purpose of the present patent application narrow throat653 is specified as a fragment of the inner tunnel having imaginaryinlet 6531 and outlet 6532, wherein the term “principal interval” ofx-axis has a sense as corresponding to the interval occupied by thespecifically shaped tunnel, i.e. at least comprising narrow throat 653.

FIG. 6g , in conjunction with FIG. 6f , is a schematic graphicillustration of the distribution of the fluid 651's three parameters:velocity 660, static pressure 670, and temperature 680 along the lengthof nozzle 650 calculated according to equations (6.11) and (6.13).

The narrowest cross-section of the throat 653 (FIG. 6f ) provides the“critical condition” point 658, triggering the inverse de Lavaljet-effect, according to equation (6.13), that is observed as an effectof flow slowing, when the flow moves along convergent funnel 652, andfurther slowing, when the flow moves through the divergent stage ofconvergent-divergent jet-nozzle 650 downstream-behind the criticalcondition point 658. For the purposes of the present patent application,the term “de Laval retarding-effect” is introduced as relating to theinverse de Laval jet-effect. Fast fluid-flow 651 moves along convergentfunnel 652, where, ahead of the critical condition point 658 of narrowthroat 653, the velocity falls 661, and the pressure and temperaturepick up, correspondingly 671 and 681. The velocity falls 661 such thatM-velocity M₆₆₃, corresponding to marker 663, reaches the specificM-velocity M*=√{square root over ((γ−1)/γ)} at the critical conditionpoint 658. Fluid-flow 651 exits throat 653 and enters the wideningdivergent exhaust tailpipe 654, where fluid-flow 651 is subjected toincrease of cross-sectional area, and this action is optimized such thatthe decrease of M-velocity 662 is accompanied by a substantiallysmoothed increase of the pressure and temperature, 672 and 682,correspondingly. Slow hot and compressed fluid at position 656 outflowsfrom wide exhaust tailpipe 654. Again, the smoothed change of staticpressure 670 provides a suppression of unwanted Mach waves. In practice,the suppression of Mach waves provides a suppression of undesiredvibrations that, in particular, especially important for a fastdecelerating flying vehicle.

In view of the foregoing description referring to FIGS. 6f and 6g , itwill be evident to a person skilled in the art that, on the one hand, totrigger the de Laval retarding-effect the high M-velocity M₆₅₁ must below sufficient to reach the specific M-velocity M* while slowing inconvergent funnel 652 and the convergent stage of throat 653. On theother hand, taking into account that, in practice, for the case whereinfluid-flow 651 is an airflow, the M-velocity is distributed in thedirection normal to an adjacent surface such that decreases almost downto zero at the surfaces of convergent-divergent jet-nozzle 650's walls.Thus, a certain portion of fast fluid-flow 651 at the critical conditionpoint 658 moves with the effective M-velocity equal to the specificM-velocity M* and is subjected to a convergent-divergent reshaping inthroat 653, thereby, the conditions for the de Laval retarding-effecttriggering is satisfied for any high M-velocity M₆₅₁, higher than thespecific M-velocity M*.

In view of the foregoing description referring to FIGS. 6a, 6b, 6f and6g and derivation of equations (6.8) and (6.9), the de Laval jet-effectand the de Laval retarding-effect, both observed in the case of aconverging flow, are specified as the following. The de Laval jet-effectis specified as an effect of a convergent flow portion convectiveacceleration, occurring, when the convergent flow portion moves withM-velocities lower than the specific M-velocity upstream-afore thecritical condition point, reaches the specific M-velocity at thecritical condition point, and moves with M-velocities higher than thespecific M-velocity downstream-behind the critical condition point; andthe de Laval retarding-effect is specified as an effect of a convergentflow portion warming and slowing, occurring, when the convergent flowportion moves with M-velocities higher than the specific M-velocityupstream-afore the critical condition point, reaches the specificM-velocity at the critical condition point, and moves with M-velocitieslower than the specific M-velocity downstream-behind the criticalcondition point.

For the purposes of the present patent application, the terms “VenturiM-velocity”, “de Laval M-velocity”, “de Laval low M-velocity”, and “deLaval high M-velocity” should be understood as the following:

-   -   a Venturi M-velocity is defined as an M-velocity, lower than the        specific M-velocity M* and low sufficient to cross a narrow        throat with said M-velocity, lower than the specific M-velocity        M*;    -   a de Laval low M-velocity is defined as an M-velocity lower than        the specific M-velocity M* and high sufficient to reach the        specific M-velocity M* at the critical condition point x*;    -   a de Laval high M-velocity is defined as an M-velocity higher        than the specific M-velocity M* and low sufficient to reach the        specific M-velocity M* at the critical condition point x*; and    -   a de Laval M-velocity is at least one of the de Laval low        M-velocity and the de Laval high M-velocity.

In view of the foregoing description referring to FIGS. 6f and 6g , itwill be evident to a person skilled in the art that one can optimize thespecifically shaped tunnel of convergent-divergent jet-nozzle 650providing such a conformity of the cross-sectional area of the openinlet with the de Laval high M-velocity of flowing fluid crossing theopen inlet, that the flowing fluid M-velocity is substantially smooth atthe entering the open inlet. Furthermore, one can control thecross-sectional area of open inlet, according to the equation ofprinciple, providing conformity of the open inlet cross-sectional areawith the variable M-velocity of the entering flowing fluid. This maybecome important, for example, to suppress vibrations of a fast slowingvehicle.

Two-Stage Convergent-Divergent Jet-Nozzle

FIG. 6h is a schematic illustration of a two-stage convergent-divergentjet-nozzle 690 exposed to an incoming fast fluid-flow 691, streamingwith a high M-velocity M₆₉₁, higher than the specific M-velocityM*=/√{square root over ((γ−1)/γ)}, i.e. with a de Laval high M-velocity.Two-stage convergent-divergent jet-nozzle 690, constructed according tothe principles of a preferred embodiment of the present invention, hasan inner tunnel comprising the first and second convergent-divergentstages, separated by widened reservoir 694. The firstconvergent-divergent stage performs the first-stage convergentinlet-funnel 692 gradually turning into the first-stage narrowconvergent-divergent throat 693 having a local narrowest cross-sectionproviding the first critical condition point 6981 and having aninverse-funnel shaped pipe leading to widened reservoir 694. The secondconvergent-divergent stage comprises the second-stage narrow throat 696,having a local narrowest cross-section providing the second criticalcondition point 6982, and the second-stage divergent exhaust tailpipe697.

Incoming fast fluid-flow 691 is gradually slowing down, becoming warmerand more thickened and compressed as moving along the firstconvergent-divergent stage to widened reservoir 694 as describedhereinbefore with reference to FIGS. 6f and 6g . Slow, hot andcompressed fluid 695 further movies through the secondconvergent-divergent stage. The fluid flow is accelerating as movingthrough throat 696, where exceeds the specific M-velocity M*=√{squareroot over ((γ−1)/γ)} downstream-behind the second critical conditionpoint 6982. Jetstream 699 outflowing through divergent exhaust tailpipe697, is faster and colder than slow, hot and compressed fluid 695, yetto be entered into the second convergent-divergent stage, as describedhereinbefore tracing after incoming compressed and hot airstream 611with reference to FIGS. 6a and 6b . Fast outflowing jetstream 699 has across-section wider than incoming fast fluid-flow 691 at the input ofconvergent inlet-funnel 692. So, the M-velocity M₆₉₉ of fast outflowingjetstream 699 is higher than the M-velocity M₆₉₁ of fast fluid-flow 691,according to equation (6.13).

Thereby, two-stage convergent-divergent jet-nozzle 690 operates as ajet-booster based on the de Laval enhanced jet-effect launchingoutflowing jetstream 699, which is faster than fast fluid-flow 691incoming with the de Laval high M-velocity M₆₉₁, i.e. higher than thespecific M-velocity M*=√{square root over ((γ−1)/γ)}. This is one moreteaching of the present invention.

Optimal Implementation of Convergent-Divergent Jet-Nozzle

FIG. 7a shows comparative graphs 700 for the dependencies of the nozzletunnel extension ratio vs. the airflow M-velocity, calculated by theclassical and suggested models, namely, curves 703 and 704correspondingly; wherein the vertical axis 701 is the ratio A/A*, andthe horizontal axis 702 is the airflow M-velocity measured intemperature dependent Mach numbers. The dashed curve 703 is theconvergent-divergent cross-sectional area ratio A/A* profile vs. theairflow M-velocity, calculated using equation (1) derived from the Eulerequations of fluid motion. The solid curve 704 is theconvergent-divergent cross-sectional area ratio A/A* profile vs. theairflow M-velocity, calculated using suggested equation (6.13) derivedfrom the generalized equations of fluid motion. The critical conditionpoint 708 corresponds to the specific M-velocity M*=√{square root over((γ−1)/γ)}≈0.5345. Comparative graphs 700 show that one needs in asubstantially extra-widened nozzle tunnel 704 to reach the airflowM-velocities substantially higher than 1 Mach.

Therefore, a convergent-divergent jet-nozzle, constructed according toan exemplary embodiment of the present invention, allows increasedefficiency of the jet-effect for use at high-subsonic, transonic,supersonic, and hypersonic velocities that can be applied to rocketnozzle design.

Taking into account relation (6.11), one can derive equations bondingthe exhaust-nozzle outlet M-velocity M_(e) with the ratios P₀/P_(e) andT₀/T_(e), where P_(e) and T_(e) are correspondingly the static pressureand temperature at the exhaust-nozzle tunnel outlet:

$\begin{matrix}{M_{e} = {\sqrt{\frac{2}{\gamma}}\sqrt{\left( \frac{P_{0}}{P_{e}} \right)^{\frac{\gamma - 1}{\gamma}} - 1}}} & {{Eq}.\mspace{14mu}\left( {7.1a} \right)} \\{\frac{P_{0}}{P_{e}} = \left( \frac{2 + {\gamma\; M_{e}^{2}}}{2} \right)^{\frac{\gamma}{\gamma - 1}}} & {{Eq}.\mspace{14mu}\left( {7.1b} \right)} \\{\frac{T_{0}}{T_{e}} = \left( \frac{2 + {\gamma\; M_{e}^{2}}}{2} \right)} & {{Eq}.\mspace{14mu}\left( {7.1c} \right)} \\{\frac{\rho_{0}}{\rho_{e}} = \left( \frac{2 + {\gamma\; M_{e}^{2}}}{2} \right)^{\frac{1}{\gamma - 1}}} & {{Eq}.\mspace{14mu}\left( {7.1d} \right)}\end{matrix}$

In contrast to the classical theory, saying that both: the de Lavaljet-effect and the velocity of sound are reachable when the ratioP₀/P_(e) is of 1.893, equation (7.1b) shows that, on the one hand, toobtain the de Laval jet-effect [i.e. condition M_(e)≥M*] for air using anozzle tunnel having an optimal convergent-divergent shape, one mustprovide the ratio P₀/P* at least of 1.893, and, on the other hand, toaccelerate an air portion up to the velocity of sound [i.e. M_(e)=1],one must provide the ratio P₀/P_(e) at least of 6.406. Equation (7.1c)says that, on the one hand, to obtain the de Laval jet-effect for airutilizing a nozzle tunnel having optimal convergent-divergent shape, onemust provide the ratio T₀/T, at least of 1.2; and, on the other hand, toaccelerate an air portion up to the velocity of sound, one must providethe ratio T₀/T_(e) at least of 1.7. So, the principle condition either1.893<P₀/P_(e)<6.406 or/and 1.2<T₀/T_(e)<1.7 may provide the de Lavaljet-effect occurring without the phenomenon of shock sound-wave emissionthat is one of the primary principles of the present invention.

Thus, a convergent-divergent jet-nozzle tunnel, constructed according toan exemplary embodiment of the present invention and exploited inaccordance with the principle conditions, allows an optimalimplementation and efficient use of an enhanced jet-effect at de LavalM-velocities.

Vortex Tube as Convergent-Divergent Jet-Nozzle

Reference is now made again to prior art FIG. 1l , showing vortex-tube190, and FIG. 6a , showing convergent-divergent jet-nozzle 610constructed according to an exemplary embodiment of the presentinvention.

Point out that the vortex tube 190's exhaust tunnels to outlets 317 and318 can be considered as converging and convergent-divergent jet-nozzlescorrespondingly at heating and cooling ends.

Consider, for simplicity, the nozzle effect only at outlet 19.8. Applyestimations (7.1a,b,c) to an ideal construction of vortex tube 190 andtake into account the aforementioned conditions of exploitation. Namely,entering air 310 has the pressure of P₀=6.9 bar, while the value P_(e)is about 1 bar such that P₀/P_(e) is substantially higher than 1.893that provides M-velocity of M*=√{square root over ((γ−1)/γ)} into the“throat” 19.9. Moreover, the estimated ratio P₀/P_(e)˜6.4 says that ifthe widening exhaust tunnel, having outlet 19.8 diameter greater thaninner diameter 19.9 would be constructed in accordance with an exemplaryembodiment of the present invention similar to convergent-divergentjet-nozzle 610 (FIG. 6a ) such that A_(e)/A*≈1.5197, then outlet 19.8M-velocity is expected to be approximately of M_(e)≈1. In this case, itfollows from (7.1c) that the reachable temperature ratio isT₀/T_(e)=1.7. I.e., if T₀=21° C.=294.14° K, then T_(e)≈173° K≈−100° C.This estimation shows that:

-   -   first, the novel explanation of the well-known vortex-tube        effect by the dominant phenomenon occurred in the de Laval        convergent-divergent jet-nozzle is confirmed by calculations        based on equations (7.1a,b,c); and    -   second, a cooling temperature, substantially lower than the        aforementioned “−34° C.”, is reachable by optimizing the        mentioned outlet convergent-divergent tunnel shape.

Thus, a convergent-divergent jet-nozzle, constructed and exploitedaccording to an exemplary embodiment of the present invention, allowsoptimizing the efficiency of an enhanced jet-effect use to launch anextra-cooled gas outflow.

Compressor Supplied by Convergent-Divergent Jet-Nozzle

FIG. 7b is a schematic illustration of a hypothetically optimalconvergent-divergent jet-nozzle 710 with the critical condition point718 applied to accelerate air portion 711, constructed according to theprinciples of the present invention. Air portion 711 is compressed andheated in a reservoir 712. To compress air portion 711 up to pressureP₀=6.4 bar one needs to consume the energy E₀ estimated as (P₀−P_(e))V₀,where V₀ is the volume of the gas reservoir 712. For V₀=1 m³, the energyE₀ is estimated as E₀≈5.4×10⁵ J=540 kJ. The volume V₀ is composed ofapproximately n≈(P₀/P_(e))×1000/22.4=286 moles of gas. When air portion711 is accelerated and expanded in de Laval-like nozzle 710, it acquireskinetic energy at the expense of thermodynamically related pressure andtemperature decrease; wherein the pressure decreases from P₀ to P_(e)and the temperature decreases from T₀ to T_(e). Let air portion 711accelerate in hypothetically optimal convergent-divergent jet-nozzle 710such that the velocity of the outflowing stream 713 is almost as thespeed of sound, i.e. the exhaust M-velocity is of Me 1. ThenT₀/T_(e)=1.7 and (T₀−T_(e))=T₀(1−1/1.7)=0.412T₀. In this case, theacquired kinetic energy equals K=n×(T₀−T_(e))R that is estimated as:K=n×0.412T ₀ R≈286×0.412×298×278≈9,761,674 J=9,762 kJ.

This estimation shows that the triggered acquired kinetic energy K mayexceed the triggering consumed energy E₀ at least at subsonic velocitiesby the factor of 18 times. The acquired kinetic energy can be applied toa vehicle motion or to an engine for electricity generation withpositive net-efficiency. On the other hand, the acquiring of kineticenergy is accompanied by the air temperature decrease, therefore, such aconvergent-divergent jet-nozzle can be applied to cooling of a vehicleengine as well as be used either for electricity harvesting by means ofa Peltier element operating as thermoelectric generator and/or as aneffective condenser of vapor to water.

Flying Capsule as Dragging-Jet Engine

FIG. 7c is a schematic sectional view of a flying capsule corpus 720 ina sagittal plane. Capsule corpus 720, constructed according to theprinciples of the present invention, has outer airfoil side 729 andcomprises an inner converging reservoir 721 as a dragging compressorhaving an open inlet 725 exposed to ambient wind 724 and further havinga hypothetically optimal convergent-divergent tunnel 722 with a narrowthroat comprising a critical condition point 728 and divergent exhausttailpipe having an open outlet 726 of area A_(e). The velocity ofambient air 724 relative to capsule 720 is u_(a) which is substantiallylower than the critical condition velocity u*, corresponded to thespecific M-velocity M*=√{square root over ((γ−1)/γ)}. The wind portion727 enters the inner converging reservoir 721 with the velocity equal tou_(in). The area A_(in) of inlet 725 is substantially wider than thearea A* of the throat's cross-section at the critical condition point728 such that air portion 727 crosses the area A* at the criticalcondition point 728 with the maximal reachable M-velocity equal to thespecific M-velocity M*=√{square root over ((γ−1)/γ)}, and so the deLaval enhanced jet-effect is expected in the divergent exhaust tailpipehaving outlet 726, where the velocity of outflowing jetstream 723reaches a value u_(e) higher than the velocity u, corresponding to thecritical condition point 728. In an exemplary embodiment of the presentinvention, an optimal shape of tunnel 722 provides that the value u_(e)is lower than the speed of sound u_(sound). Outflowing jetstream 723brings the kinetic power acquired at the expense of the flow warmth. Theacquired kinetic power of outflowing jetstream 723 may be high as oreven become higher than the power consumed to compensate drag, definedby a drag coefficient corresponding to a concave shape of the innerconverging reservoir 721, and thereby to maintain the flying velocityu_(a) of capsule 720. Capsule 720 is interpreted as a motionlessdragging-jet engine.

Outer airfoil side 729 of capsule corpus 720 provides laminar-likeflowing of wind outer sub-portions 731 and 732, moving adjacent to outerairfoil side 729 and being subjected to the Coanda-effect operation and,thereby, attracted to the nearby surfaces of outer airfoil side 729.Outflowing jetstream 723 having the decreased static pressure sucksouter sub-portions 731 and 732. The cumulative confluence ofsub-portions 731, 732, and 723 constitutes cumulative jetstream 734,associated with the airfoil corpus of capsule 720. In general, theformed cumulative jetstream 734, composed of sub-portions 731, 732, and723, is turbulent; however, in an optimal case, the turbulence can besuppressed substantially. For simplicity, consider a case of alaminar-like cumulative jetstream 734, “bordered” by streamlines 733. Onthe one hand, the velocities of outer sub-portions 731 and 732, beinglower than the critical condition velocity u*, are increasing as theattracted outer sub-portions enter the space of cumulative jetstream734, where the velocities increase is accompanied by a constriction ofouter sub-portions 731 and 732, in accordance with equation (6.13). Onthe other hand, at outlet 726, the velocity of inner sub-portion 723 isof value u_(e) higher than the critical condition velocity u*. Accordingto equation (6.13), the velocity of inner sub-portion 723 is decreasingas the sub-portion enters the space of cumulative jetstream 734, whereinner sub-portion 723 is constricting as well. If the case is optimizedsuch that the both constrictions are identical, cumulative jetstream 734is expected to be laminar-like indeed. Bordering streamlines 733constitute an imaginary convergent-divergent jet-nozzle comprising anarrow throat having the minimal cross-sectional area at the outercritical condition point 738, where the effective M-velocity ofcumulative jetstream 734 reaches the specific value M*=√{square rootover ((γ−1)/γ)}. If, upstream-afore the outer critical condition point738, the effective M-velocity of cumulative jetstream 734 is lower thanthe specific M-velocity M*, then the M-velocity of cumulative jetstream734 is increasing as cumulative jetstream 734 moves such that outflowingdivergent portion 735 has M-velocity higher than M* downstream-behindthe outer critical condition point 738; and vice versa, if,upstream-afore the outer critical condition point 738, the effectiveM-velocity of cumulative jetstream 734 is higher than the specificM-velocity M*, then the M-velocity of cumulative jetstream 734 isdecreasing as cumulative jetstream 734 moves such that outflowingdivergent portion 735 has the M-velocity lower than the specificM-velocity M*.

In view of the foregoing description referring to FIG. 7c , it will beevident to a person skilled in the art that:

-   -   The shape of tunnel 722 can be optimized to provide that the        velocity value u_(e) of outflowing jetstream 723 becomes higher        than the speed of sound u_(sound). As well, it will be evident        to a person skilled in the art that the shape of tunnel 722 and        outer airfoil side 729 of capsule 720 can be optimized to        provide that outflowing divergent portion 735 has increasing        M-velocity reaching values higher than the specific M-velocity        M*;    -   Supplying a flying vehicle or helicopter's propeller blades by        nozzles similar to capsule 720 operating as jet-booster, one        could save fuel consumption substantially and even provide a        stable motion against a drag and skin-friction resistance        entirely with no fuel burning at all. As well, it will be        evident to a person skilled in the art that this is not a        so-called “Perpetuum mobile”, but a use of ambient fluid heat to        produce useful motion, strongly according to the Energy        Conservation Law. Furthermore, looking ahead referring to FIGS.        9d, 9e, and 9f described hereinafter, point out that an even        number of such jet-boosters, attached to the even number of        blades of a helicopter's propeller, result in stabilization of        the effective velocities of incoming and outflowing jetstreams        associated with the jet-boosters. The predictably equalized        velocities enable easier controllable lift-forces when the        helicopter is flying speedily;    -   The described airfoil capsule can be stationary exposed to        oncoming wind (either natural or artificial) and thereby become        applicable to an efficient harvesting of electricity providing a        positive net-efficiency; and    -   One can further aggregate the open outlet of a specifically        shaped convergent-divergent tunnel with an engine using the        enhanced jet-effect providing an extra-accelerated and        extra-cooled jetstream outflowing through the open outlet;        wherein the engine is either a jet-engine, and/or a turbo-jet        engine, and/or a motor applied to a vehicle, and/or a generator        of electricity, and/or a cooler, and/or a Peltier element        operating as thermoelectric generator, and/or vapor-into-water        condenser.

FIG. 7d is a schematic sectional view of a flying capsule 740,constructed according to the principles of the present invention. Flyingcapsule 740's profile in a sagittal plane has an airfoil outer contourand a contour of a specifically shaped two-stage inner tunnel. Incontrast to flying capsule 720 illustrated hereinbefore referring toFIG. 7c , capsule 740 flies with a de Laval high M-velocity, i.e. higherthan the specific M-velocity M*=√{square root over ((γ−1)/γ)}, and thetwo-stage inner tunnel is shaped similar to the tunnel of two-stageconvergent-divergent jet-nozzle 690, described above with reference toFIG. 6h . Namely, the two-stage inner tunnel comprises two narrowthroats providing for two associated critical condition points 741 and742. The oncoming fast flow 743 enters the open inlet 744 of the innertunnel with a de Laval high M-velocity, higher than the specificM-velocity M*. Then flow 743 is gradually slowing down, becoming warmerand more compressed as moving to critical condition point 741 wherereaching the specific M-velocity M*, further, is graduallyextra-slowing, extra-warming and extra-compressing as moving toreservoir 745, according to equation (6.13), further, is graduallyaccelerating, cooling, and becoming decompressed as moving to criticalcondition point 742 where again reaching the specific M-velocity M*, andfurther, is gradually extra-accelerating, extra-cooling, andextra-decompressing as moving to outlet 746, as described hereinbeforewith references to FIGS. 6a, 6b, 6f, 6g , and 6 h.

The cross-section of outlet 746 is wider than the cross-section of inlet744, thereby providing for that capsule 740 operates as a jet-boosterlaunching a widened and cooled outflowing jetstream 747 with a highM-velocity, higher than the de Laval high M-velocity of oncoming fastflow 743.

Improved Propeller and Ventilator

FIG. 7e is a schematic drawing of improved blowing propeller orventilator 770, constructed according to the principles of the presentinvention, to operate in fluid surroundings. For simplicity and withoutloss of the description generality, consider improved blowing ventilator770 operating in an open air space. Improved blowing ventilator 770,defined by the main functionality to launch a jetstream characterized bythe flow headway-motion kinetic-power, has an inherent engine, which isnot shown here, consuming either a power of burned fuel or an electricalpower and operating in a steady-state mode. Improved blowing ventilator770 comprises airfoil blades: first-airfoil-blades 772.1 andsecond-airfoil-blades 772.2, shown here schematically, each, whencompounded with imaginary sagittal axis 771, having a chiralasymmetrical shape, wherein, preferably, the shape offirst-airfoil-blades 772.1 is substantially mirror-symmetrical relativeto the shape of second-airfoil-blades 772.2. First-airfoil-blades 772.1and second-airfoil-blades 772.2 are forcedly rotating in transitionalspace “T7”, marked schematically as a cylindrical space portion betweenfrontal planes 779.1 and 779.2. Mutually complementalfirst-airfoil-blades 772.1 and second-airfoil-blades 772.2 are forcedlyrotating in mutually-opposite directions, indicated by curved arrowsmarked by reference numerals 773.1 and 773.2, correspondingly. Forcedlymutually-opposite rotating first-airfoil-blades 772.1 andsecond-airfoil-blades 772.2 cover effective cross-section 774, and,thereby, entrap and suck air portions 775.A from space “A7”, which islocated upstream-afore effective cross-section 774, and convert flowingair portions 775.A into accelerated jetstream 775.B entering space “B7”,which is located downstream-behind effective cross-section 774. Space“A7”, comprising airflow portions 775.A subjected to the sucking andmotion through effective cross-section 774, is bordered by streamlinesof airflow 775.A, forming imaginable contours 776.A. The imaginarycontours 776.A separate space “A7” from space “C7”, comprising airportions 775.C, drawn by airflow 775.A and flowing toward transitionalspace “T7” out of effective cross-section 774. Space “B7”, comprisingjetstream 775.B, is bordered by streamlines, forming imaginable contours776.B. The imaginary contours 776.B separate space “B7” from space “D7”,comprising air portions 775.D, drawn by jetstream 775.B and flowingdownstream-behind transitional space “T7”. In contrast to the generalcase, when a complicated motion of air portions 775.A, 775.B, 775.C, and775.D comprises both: a headway-motion, i.e. a laminar component ofmotion aligned with the imaginary contours 776.A and 776.B having aprevalent direction along imaginary sagittal axis 771, and awhirling-motion, i.e. a turbulent component of motion, dominantly,whirling around imaginary sagittal axis 771; the forcedlymutually-opposite rotating first-airfoil-blades 772.1 andsecond-airfoil-blades 772.2 are optimized to prevent the power-consumingwhirling motion and provide the desired dominant headway-motion of airportions 775.A, 775.B, 775.C, and 775.D, as one of the primary featuresof improved blowing ventilator 770. For simplicity, further describingthe optimized case, minor effects caused by the whirling turbulence willbe ignored. In the optimized case, the power, consumed by the inherentengine of improved blowing ventilator 770, dominantly, is expended for:

-   -   the headway-motion of air portions 775.A, which then are        transformed into jetstream 775.B;    -   the directional motion of air portions 775.C, which then are        transformed into moving air portions 775.D;    -   the overcoming of air viscous-resistance; and    -   the compensation of inner resistance of the inherent engine.        Wherein the part of the power consumption, expended on the        overcoming of air viscous-resistance and compensation of inner        resistance of the inherent engine, dissipates in the acquired        warmth of outflowing air portions 775.B and 775.D.        Mutually-opposite rotating first-airfoil-blades 772.1 and        second-airfoil-blades 772.2 have optimized shapes, in addition        providing a certain focusing of jetstream 775.B, such that        streamlines 776.A and 776.B constitute an imaginary        convergent-divergent tunnel. Furthermore, the speeds of        first-airfoil-blades 772.1 and second-airfoil-blades 772.2        mutually-opposite rotations are optimized such that jetstream        775.B moves through cross-section 778.B of the minimal area with        the specific M-velocity M*=√{square root over ((γ−1)/γ)},        thereby making the imaginary convergent-divergent tunnel,        constituted by streamlines 776.A and 776.B, in principle,        similar to the specifically shaped tunnel of        convergent-divergent jet-nozzle 610 shown in FIG. 6a , wherein        imaginary sagittal axis 771 and imaginary sagittal x-axis 615        (FIG. 6a ) are collinear, effective cross-section 774 takes the        place of imaginary inlet 6131 (FIG. 6a ), and cross-section        778.B of the minimal area provides the critical condition for        the de Laval effect triggering. Thus, the imaginary        convergent-divergent tunnel, constituted by streamlines 776.A        and 776.B, performs a de Laval-like nozzle. A de Laval-like        jet-effect, which is similar to the classical de Laval        jet-effect but arising in the de Laval-like nozzle having        imaginary walls formed by streamlines 776.A and 776.B of the        flowing air, is triggered, as described hereinbefore referring        to FIGS. 6a, 6b, 6c, 6d, and 6e , thereby resulting in an        extra-acceleration and extra-cooling of jetstream 775.B        immediately downstream-behind cross-section 778.B. This provides        one of the primary features of improved blowing ventilator 770.

The de Laval-like nozzle, having imaginary convergent-divergent tunnelformed by streamlines 776.A and 776.B of the flowing air, geometrically,is not identical with an optimized de Laval nozzle having solid walls,described hereinbefore referring to FIGS. 6a, 6b, 6c, 6d, and 6e , atleast because of the osmotic-like effect inherently occurring onimaginary contours 776.A and 776.B, as described above with referencesto FIGS. 4 and 5 b. The osmotic-like effect is defined as an effect ofexchange of molecular matter and heat between moving air portions. Theosmotic-like effect includes a mutually-directed effect of diffusion,occurring because of both: the Brownian random motion of the fluid'smolecules, and the effect of molecules motion in a cross-sectionalplane, caused by the gradients of fluid density Δρ and temperature ΔT inthe cross-sectional plane, which are interrelated with the jetstream775.B convergent-divergent motion. The osmotic-like effect, reducing thegradients, is accumulative, making equation (6.13) applicablequalitatively to a local neighborhood of a coordinate at sagittal axis771 only.

Since a certain distance downstream-behind cross-section 778.B ofminimal area, namely, in transitional space “E7”, marked schematicallyas a cylindrical space portion between frontal planes 779.3 and 779.4,the extra-accelerated jetstream 775.B, subjected to a diffusion ofmolecules of air portions 775.D as the airflow moving along sagittalaxis 771, becomes transformed into transitional jetstream 775.E,characterized by a local maximum of cross-sectional area, where thedensity and temperature of transitional jetstream 775.E are already notreducing and a high M-velocity of transitional jetstream 775.E, beinghigher than the specific M-velocity M*=√{square root over ((γ−1)/γ)}, isnot increasing more.

Farther, in space “F7” located downstream-behind transitional space“E7”, transitional jetstream 775.E is transformed into slowing jetstream775.F, which, according to equation (6.13) qualitatively applicable to alocal neighborhood, is characterized by an increase of airflow densityand temperature. Slowing jetstream 775.F, bordered byconvergent-divergent streamlines 776.F, reaches cross-section 778.F ofminimal area, where the M-velocity of jetstream 775.F reverts to thespecific M-velocity M*=√{square root over ((γ−1)/γ)} and the deLaval-like retarding-effect is triggered resulting in an extra-slowingand extra-warming of jetstream 775.F downstream behind cross-section778.F of minimal area, as described hereinabove referring to FIGS. 6fand 6g , relating to jet-nozzle 650, having solid walls.

Gradual variations of the air thermodynamic parameters are expected inthe open space, thereby providing optimized shapes of imaginary contours776.A, 776.B, 776.E, and 776.F. These optimizations result in thatimproved blowing ventilator 770:

-   -   on the one hand, powered by the inherent engine, expends the        power for:        -   the headway-motion of air portions 775.A, further            transformed into directional jetstreams 775.B, 775.E, and            775.F,        -   the directional motion 775.C, further transformed into            directional motion 775.D,        -   the overcoming of air viscous-resistance, and    -   the compensation of inner resistance of the inherent engine; and    -   on the other hand, triggering the de Laval-like jet-effect in an        adiabatic process, saves the power for the jetstream 775.B        acceleration and extra-acceleration, correspondingly,        upstream-afore and downstream-behind cross-section 778.B,        providing one of the primary features of improved blowing        ventilator 770.

The resulting functionality net-efficiency of improved blowingventilator 770 is defined by the ratio of the kinetic-power of launchedjetstream 775.E to the power, consumed by the inherent engine ofimproved blowing ventilator 770.

In view of the foregoing description referring to FIG. 7e , it will beevident to a person skilled in the art that improved blowing ventilator770 provides for jetstream 775.B launching and further acceleration andextra-acceleration at the expense of both: the power of inherent engineand the warmth of ambient air, so the resulting functionalitynet-efficiency of improved blowing ventilator 770 may exceed 100%.Furthermore, improved blowing propeller 770, having the resultingfunctionality net-efficiency higher than 100% and pushing a vehicle, inthe final analysis, can operate at the expense of ambient warmth only.

In view of the foregoing description referring to FIG. 7e , it will beevident to a person skilled in the art that, to implement an improvedblowing ventilator, having real corpus 777 occupying a certain space,comprising a part of transitional space “T7”, one should implement realcorpus 777 as a fragment of a convergent-divergent tunnel for airportions 775.A and jetstream 775.B, applying principles of the presentinvention to an optimization of the tunnel shape, in order to suppressundesired power-consuming shock and Mach waves, as described hereinabovereferring to FIGS. 6a, 6b, 6c, 6d, and 6e . As well, it will be evidentto a person skilled in the art that real corpus 777 of an improvedblowing ventilator may have real walls, occupying also substantialportions of spaces “A₇” and “B7”, implementing optimized contours 776.Aand 776.B now becoming actual, such that the improved blowing ventilatorcomprises a real specifically shaped convergent-divergent tunnel havingnarrow throat with the critical condition point, as describedhereinabove referring to FIG. 6a . As well, it will be evident to aperson skilled in the art that an improved blowing ventilator can beused to accelerate and focus an ionized gas, i.e. plasma, controlled byan external magnetic field, wherein geometry of the imaginary walls,formed by streamlines 776.A and 776.B, can be controlled by the magneticfield, such that the imaginary walls, occupying substantial portions ofspaces “A₇” and “B7”, form a specifically shaped convergent-divergenttunnel having narrow throat with the critical condition point, asdescribed hereinabove referring to FIG. 6 a.

In view of the foregoing description referring to FIG. 7e , it will beevident to a person skilled in the art that one can implementtransitional space “T7” of an improved propeller, characterized by theprimary features of improved blowing ventilator 770, using a pair ofrotating airfoil Archimedes screws having helically coiledairfoil-profiled walls, similar to walls of spirals 592 and 593,described hereinbefore referring to FIG. 5i , instead of the use ofrotating first-airfoil-blades 772.1 and second-airfoil-blades 772.2. Aswell, transitional space “T7” can be implemented using a combination ofmany rotating airfoil blades and stationary or rotating airfoil screwsof Archimedes.

FIG. 7f is a schematic drawing of improved sucking propeller orventilator 780, constructed according to the principles of the presentinvention to operate in fluid surroundings. For simplicity and withoutloss of the description generality, consider improved sucking ventilator780 operating in an open air space. Improved sucking ventilator 780 isdefined by the main functionality, being inverse to the mainfunctionality of improved blowing ventilator 770, described above withthe reference to FIG. 7e , namely, to make an incoming jetstream,characterized by the flow headway-motion kinetic-power. Looking ahead,point out that improved sucking ventilator 780, constructed according tothe principles of the present invention, is as inverse improved blowingventilator 770. Improved sucking ventilator 780 has an inherent engine,which is not shown here, consuming either a power of burned fuel or anelectrical power and operating in a steady-state mode. Improved suckingventilator 780 comprises airfoil blades: first-airfoil-blades 782.1 andsecond-airfoil-blades 782.2, which are shown schematically, each havingan asymmetrical and chiral geometrical configuration, wherein,preferably, the geometrical configuration of first-airfoil-blades 782.1is mirror-symmetrical relative to the geometrical configuration ofsecond-airfoil-blades 782.2. Mutually complemental first-airfoil-blades782.1 and second-airfoil-blades 782.2 are forcedly rotating intransitional space “T8”, marked schematically as a cylindrical spaceportion between frontal planes 789.1 and 789.2. First-airfoil-blades782.1 and second-airfoil-blades 782.2 are forcedly rotating inmutually-opposite directions, indicated by curved arrows marked byreference numerals 783.1 and 783.2, correspondingly.First-airfoil-blades 782.1 and second-airfoil-blades 782.2 havegeometrical configurations such that, when forcedly mutually-oppositerotating and covering effective cross-section 784, entrap and suckincoming jetstream 785.B from space “B8”, which is locatedupstream-afore effective cross-section 784, convert incoming jetstream785.B into defocusing airflow 785.A, divergently entering space “A₈”,which is located downstream-behind effective cross-section 784.

Incoming jetstream 785.B, subjected to the sucking, is bordered bystreamlines forming imaginary contours 786.B. The imaginary contours786.B separate space “B8” from space “D8”, comprising air portions785.D, drawn by incoming jetstream 785.B and flowing toward transitionalspace “T8” out of effective cross-section 784. Space “A8”, comprisingdivergent airflow 785.A, is bordered by streamlines forming imaginarycontours 786.A. The imaginary contours 786.A separate space “A8” fromspace “C8”, comprising air portions 785.C, drawn by divergent airflow785.A and flowing downstream-behind transitional space “T8”. Forcedlymutually-opposite rotating first-airfoil-blades 782.1 andsecond-airfoil-blades 782.2 are optimized to prevent the power-consumingwhirling motion and provide the desired dominant headway-motion of airportions 785.A, 785.B, 785.C, and 785.D, as one of the primary featuresof improved sucking ventilator 780.

Mutually-opposite rotating first-airfoil-blades 782.1 andsecond-airfoil-blades 782.2 have optimized shapes, in addition providinga certain defocusing of incoming jetstream 775.B, such that streamlines786.B and 776.A constitute an imaginary convergent-divergent tunnel.Furthermore, the mutually-opposite rotations speeds are optimized suchthat incoming jetstream 785.B moves through cross-section 788.B of theminimal area with the specific M-velocity M*=√{square root over((γ−1)/γ)}, thereby making the imaginary convergent-divergent tunnel,constituted by streamlines 786.B and 786.A, similar to the specificallyshaped tunnel of convergent-divergent jet-nozzle 650 shown in FIG. 6f ,wherein imaginary sagittal axis 781 and imaginary sagittal x-axis 655(FIG. 6f ) are collinear, effective cross-section 784 takes the place ofimaginary outlet 6532 (FIG. 6f ), and cross-section 788.B of the minimalarea provides the critical condition for the de Laval effect triggering.Thus, the imaginary convergent-divergent tunnel, constituted bystreamlines 786.B and 786.A, performs an inverse de Laval-like nozzle. Ade Laval-like retarding-effect, which is similar to the classical deLaval retarding-effect described hereinbefore referring to FIG. 6f butoccurring in the inverse de Laval-like nozzle having imaginary wallsformed by streamlines 786.B and 786.A of the flowing air, is triggered,thereby resulting in an extra-slowing and extra-warming of incomingjetstream 785.B immediately downstream-behind cross-section 788.B.Furthermore, the condition of incoming jetstream 785.B moving throughcross-section 788.B of the minimal area with the specific M-velocityM*=√{square root over ((γ−1)/γ)} interrelates with the condition ofextra-pre-acceleration of incoming jetstream 785.B just upstream-aforecross-section 788.B, according to equation (6.13) qualitativelyapplicable to a local neighborhood. Thus, the M-velocity of incomingjetstream 785.B just upstream-afore cross-section 788.B is higher thanthe specific M-velocity M*=√{square root over ((γ−1)/γ)}. This providesone of the primary features of improved sucking ventilator 780.

Furthermore, again, according to equation (6.13) qualitativelyapplicable to a local neighborhood, the high M-velocity, higher than thespecific M-velocity M*=√{square root over ((γ−1)/γ)}, can be reached dueto the direct de Laval-like jet-effect in an earlier pre-history ofincoming jetstream 785.B, namely, in space “F8” comprising pre-incomingjetstream 785.F moving through imaginary convergent-divergent tunnelconstituted by streamlines 786.F and having cross-section 788.F of localminimum area providing the critical condition. Then the accumulativeosmotic-like effect results in that since a certain distancedownstream-behind cross-section 788.F of local minimum area, namely, intransitional space “E8”, marked schematically as a cylindrical spaceportion between frontal planes 789.3 and 789.4, pre-incoming jetstream785.F, subjected to a diffusion of air molecules as moving alongsagittal axis 781, becomes transformed into transitional jetstream785.E, characterized by a local maximum of cross-sectional area, wherethe density and temperature of transitional jetstream 785.E are alreadynot reducing and the M-velocity of transitional jetstream 785.E, beinghigher than the specific M-velocity M*=√{square root over ((γ−1)/γ)}, isnot increasing more. Transitional jetstream 785.E becomes transformedinto incoming jetstream 785.B subjected to the de Laval-likeretarding-effect resulting in incoming jetstream 785.B slowing andextra-slowing. Thus, relatively slow divergent airflow 785.A has anupstream pre-history, comprising the pre-accelerated andextra-pre-accelerated headway-motion of jetstream 785.Bdownstream-behind and upstream-afore cross-section 788.B,correspondingly, wherein gradual variations of the air thermodynamicparameters are expected in the open space, thereby providing optimizedshapes of imaginary contours 786.B and 786.A. These optimizations resultin that improved sucking ventilator 780:

-   -   on the one hand, powered by the inherent engine, expends the        power for:        -   the headway-motion of pre-incoming jetstream 785.F, further            transformed sequentially into directional motion of            transitional jetstream 785.E, incoming jetstream 785.B, and            divergent airflow 785.A,        -   the directional motion of outer portions 785.D, further            transformed into directional motion of outer portions 785.C,        -   the overcoming of air viscous-resistance, and        -   the compensation of inner resistance of the inherent engine;    -   and    -   on the other hand, triggering the de Laval-like retarding-effect        having pre-history comprising the de Laval-like jet-effect in an        adiabatic process, saves the power for the incoming jetstream        785.B motion, accelerated and pre-extra-accelerated,        correspondingly, downstream-behind and upstream-afore        cross-section 788, providing one of the primary features of        improved sucking ventilator 780.

The resulting functionality net-efficiency of improved suckingventilator 780 is defined by the ratio of the kinetic-power of suckedtransitional jetstream 785.E to the power, consumed by the inherentengine of improved sucking ventilator 780.

In view of the foregoing description referring to FIG. 7f , it will beevident to a person skilled in the art that improved sucking ventilator780 provides for pre-incoming jetstream 785.F sucking pre-accelerationand extra-pre-acceleration at the expense of both: the power of inherentengine and the warmth of ambient air, so the resulting functionalitynet-efficiency of improved sucking ventilator 780 may exceed 100%.Furthermore, improved sucking propeller 780, having the resultingfunctionality net-efficiency higher than 100% and pulling a vehicle, inthe final analysis, can operate at the expense of ambient warmth only.

In view of the foregoing description referring to FIG. 7f , it will beevident to a person skilled in the art that, to implement an improvedsucking ventilator, having real corpus 787 occupying a certain space,comprising a part of transitional space “T8”, one should implement realcorpus 787 as a fragment of a convergent-divergent tunnel for incomingjetstream 785.B and divergent airflow 785.A, applying principles of thepresent invention to an optimization of the tunnel shape, in order tosuppress undesired power-consuming shock and Mach waves, as describedhereinabove referring to FIGS. 6a, 6b, 6c, 6d, 6e, and 6f . As well, itwill be evident to a person skilled in the art that real corpus 787 ofan improved sucking ventilator may have real walls, occupying alsosubstantial portions of spaces “B8” and “A8”, implementing optimizedcontours 786.B and 786.A now becoming actual, such that the improvedsucking ventilator comprises a real specifically shapedconvergent-divergent tunnel having narrow throat with the criticalcondition point, as described hereinabove referring to FIG. 6 f.

In view of the foregoing description referring to FIGS. 7e and 7f , itwill be evident to a person skilled in the art that one can:

-   -   implement the schematically shown mutually-opposite rotating and        mutually complemental airfoil blades using many relatively small        mutually-opposite rotating and mutually complemental airfoil        blades, distributed spatially, altogether providing the        mentioned primary features of an improved blowing and/or sucking        propeller and/or ventilator;    -   cascade an improved sucking propeller and an improved blowing        propeller such that imaginary sagittal axis 771 is as a        continuation of imaginary sagittal axis 781, and space “A7”        follows downstream behind space “A8”, thereby creating a        combined improved sucking-and-blowing propeller. A vehicle,        supplied with such a combined improved sucking-and-blowing        propeller, provides for an optimized motion with a reduced drag;        and    -   implement transitional space “T7” and/or “T8” of an improved        propeller, characterized by the primary features of improved        blowing ventilator 770 and/or improved sucking ventilator 780,        correspondingly, as a not obligatorily connected transitional        space, but comprising several separate sub-spaces, each defined        by at least one smaller propeller.

In view of the foregoing description referring to FIGS. 7e and 7f , incombination with the foregoing description referring to FIGS. 5h, 5j,and 5k , it will be evident to a person skilled in the art that one canimplement a device, similar to improved blowing and/or sucking propeller770 and/or 780, correspondingly, but comprising first-airfoil-blades772.1 and/or 782.1 and second-airfoil-blades 772.2 and/or 782.2, bothremain stationary, wherein the device, having no moving parts, issubmerged in water surroundings, and wherein at least some sides of thestationary airfoil blades are covered with a hydrophobic material, thatprovides creating of a launched and/or sucked water jetstream at theexpense of the water warmth only. Furthermore, estimations, madereferring to FIG. 5h , show that a big quantity of such smallhydrophobic-propellers, in particular, comprising stationary buthydrophobic blades, altogether cumulatively functioning like an improvedlaunching and/or sucking propeller, can provide a powerful waterjetstream that can be used, in particular, for pushing a submarine atthe expense of the water warmth.

Wing as a Convergent-Divergent Jet-Nozzle

FIG. 8a is a schematic visualization 800 of an oncoming wind portion820, without loss of generality, moving horizontally. Oncoming windportion 820 comprises airflow sub-portions 821, 822, 823, and 824flowing around actually-airfoil wing 810, having a sectional profile,constructed according to the principles of the present invention. Theupper side of actually-airfoil wing 810 comprises:

-   -   (a) a forward part meeting upper sub-portion 822 having        imaginary cross-section 831;    -   (b) a withers defined as the highest point on the upper side of        the airfoil profile, where sliding sub-portion 822 has imaginary        narrowed cross-section 832, and    -   (c) a rearward part, attracting and, thereby, redirecting the        mass-center of the upper sliding sub-portion 822        backward-downward, where sliding sub-portion 822 has imaginary        widened cross-section 833.

When airflow sub-portions 821, 822, 823, and 824 are flowing aroundactually-airfoil wing 810, the streamlines [not shown here] ofsub-portions 822 and 823, flowing near actually-airfoil wing 810, arecurving in alignment with the airfoil-profile, the streamlines [notshown here] of portions 821 and 824, flowing farther fromactually-airfoil wing 810, keep substantially straight trajectoriesaligned with imaginary horizontal lines 811 and 812 correspondinglyabove and under actually-airfoil wing 810. Actually-airfoil wing 810'ssurface material properties, porosity, and structure are implementedaccording to the principles of the present invention providing that airsub-portions 822 and 823 are subjected to the Coanda-effect, defined bythe partial pressure-“c” δP_(c), rather than to the skin-frictionresistance, occurring in an imaginary boundary layer and beingquantified by the difference (a_(w)−a−δa).

Imaginary lines 811 and 812 can be considered as imaginary walls,thereby, together with the airfoil-profile forming imaginary nozzles.The upper imaginary nozzle comprises imaginary cross-sections 831, 832,and 833, and the lower imaginary nozzle comprises imaginarycross-sections 834 and 835. Cross-section 831 is wider thancross-section 832 and cross-section 832 is narrower than cross-section833, thereby, the upper imaginary nozzle has a convergent-divergentshape and sliding sub-portion 822 represents a convergent-divergentjetstream while flowing through cross-sections 831, 832, and 833.Cross-section 834 is wider than cross-section 835, so the lowerimaginary nozzle has a converging shape. Consider a case, whenactually-airfoil wing 810 flies with a de Laval low M-velocity M₈₁₀ thatis lower than the specific M-velocity M*=√{square root over((γ−1)/γ)}≈0.5345 Mach≈664 km/h, but such that sliding sub-portion 822,moving through the upper imaginary nozzle, reaches the specificM-velocity M* when passes through the narrowest cross-section 832. So,the de Laval-like jet-effect arising is expected above actually-airfoilwing 810, i.e. within the upper imaginary convergent-divergentjet-nozzle. This is accompanied by the static pressure decrease andextra-decrease, as described hereinabove with the reference to FIG. 6b ,and thereby results in the lift-effect, becoming stronger. In frames ofthe aerodynamics, one estimates the narrowest cross-section 832 linearsize, i.e. thickness of a so-called “boundary layer”, normalized to aso-called “characteristic size” of the considered wing, as proportionalto so-called Reynolds Number. As well, the thickness of boundary layercan be specified experimentally for a kind of body corpuses. In view ofthe foregoing description referring to FIG. 6a and FIG. 8a , it will beevident to a person skilled in the art that, basing on the definednarrowest cross-section 832 linear size as the thickness of boundarylayer, one can apply the equation of principle (6.13) to design animproved profile of the wing.

In view of the foregoing description referring to FIG. 8a , it will beevident to a person skilled in the art that the described de Laval-likejet-effect is similar to the classical de Laval jet-effect, but arisingin an optimized convergent-divergent tunnel having imaginary wallsformed by streamlines of a flow. Namely, the specifically shapedconvergent-divergent tunnel comprises two opposite walls; wherein one ofthe two opposite walls is constructed from a solid material and anotherof the two opposite walls is imaginary and formed by streamlines of theflowing fluid subjected to the Coanda-effect operation.

Thus, a method for a wing profile design, based on equation (6.13)according to an exemplary embodiment of the present invention, allowsoptimizing the wing airfoil shape to reach the best efficiency of thelift-effect as a result of the enhanced jet-effect occurring above thewing. The inventor points out that the profile of the actually-airfoilwing 810 designed and optimized using the equation (6.13) has a birdlikewing shape.

The Coanda-Effect Operation Providing an Imaginary Convergent-DivergentNozzle

FIG. 8b is a schematic illustration of a flying airfoil body 840 havingthe shape of an elongated drop. For simplicity and without loss ofreasoning, the shape is axis-symmetrical around the longitudinal axis841. The airfoil body 840 comprises:

-   -   a forward part meeting oncoming flow portion 851;    -   a “withers”, defined as the highest point on the upper side of        the airfoil profile, where sliding sub-portion 853 has an        imaginary narrowed cross-section 868, and    -   a rearward part.

When an oncoming air portion 851, originally having a cross-sectionalarea 861, is running at the forward part of flying body 840, it issubjected to the Coanda-effect operation resulting in air portion 851reshaping, and thereby forming an ambient-adjoining convergent-divergentjetstream, comprising sliding sub-portions: 852 being convergent, 853being narrow and having imaginary narrowed cross-section 868 of theminimal cross-sectional area, 854 being divergent, and 855 becomingconvergent due to the Coanda-effect attraction. Body 840's surfacematerial properties, porosity, and structure are implemented accordingto the principles of the present invention, thereby providing that airportion 851 is subjected to the Coanda-effect, defined by the partialpressure-“c” δP_(c), rather than to the skin-friction resistance,occurring in an imaginary boundary layer and being quantified by thedifference (a_(w)−a−δa). Furthermore, sliding sub-portions 855, jointogether, forming the resulting cumulative air portion 856. Oncoming airportion 851 and all the mentioned derivative sub-portions move withinspace “bordered” by imaginary walls marked by dashed contours 842. Theimaginary walls 842 together with the airfoil surface of body 840constitute an imaginary tunnel. The tunnel's cross-section graduallyconstricts from the inlet cross-section 862 to the narrowestcross-section 868 and then gradually widens up to the outletcross-section 863. I.e. sliding sub-portions 852 are shrinking whilereaching the withers of airfoil body 840, where the cross-sections 868of sub-portions 853 become minimal. Then, behind the withers, thecross-sections of sub-portions 854 and 855 are widening as moving.

Sliding sub-portions 855, being under the subjection of theCoanda-effect operation, turn aside in alignment with the slipperysurfaces of airfoil body 840's rearward part and join together, formingthe resulting air portion 856. It results in a convergence of resultingair portion 856, i.e. in that, cross-section 864, located fartherdownstream, becomes narrower than cross-section 863 located immediatelybehind airfoil body 840, and opposite streamline-fragments 843 form animaginary convergent funnel.

Furthermore, opposite streamline-fragments 844, which are bordering flowportion 857, constitute an imaginary divergent stage of a tunneldownstream-behind the narrowest cross-section 864.

Thereby, the converging opposite streamline-fragments 843 and divergentopposite streamline-fragments 844 together constitute the imaginaryconvergent-divergent tunnel, and, correspondingly, portions 856 and 857together constitute an outflowing convergent-divergent jetstream.

Jet-Booster Based on the Venturi Effect

First, consider a case, when airfoil body 840 flies with a VenturiM-velocity, i.e. with a low M-velocity, lower than the specificM-velocity M*=√{square root over ((γ−1)/γ)}≈0.5345 Mach, and lowsufficient to provide that M-velocity M₈₆₈ of accelerated slidingsub-portions 853, passing cross-sections 868 over the withers, andM-velocity M₈₆₄ of accelerated sub-portions 856, passing through thenarrowest cross-section 864, both remain lower than the specificM-velocity M*, i.e. M₈₆₈<M* and M₈₆₄<M*. In this case, the narrowestcross-section 864 of outflowing air portion 856 is narrower than theoriginal cross-section 861 of oncoming air portion 851, and theM-velocities M₈₆₁, M₈₆₃, M₈₆₄, M₈₆₅, and M₈₆₈, where the indicescorrespond to markers of associated cross-sections, satisfy thefollowing conditions:

-   -   M₈₆₁<M₈₆₈<M    -   M₈₆₃<M₈₆₈<M*,    -   M₈₆₃<M₈₆₄<M    -   M₈₆₁<M₈₆₄<M*, and    -   M₈₆₅<M₈₆₄<M*        Thus, body 840 operates as a jet-booster basing on the Venturi        effect occurring in the imaginary tunnel adjacent to body 840's        surfaces.

A practical application of the phenomenon that, under certainconditions, outflowing portion 856, moving through the narrowestcross-section 864, has a velocity higher than the velocity of oncomingportion 851 is one of the primary teachings of the present invention.

Jet-Boosters Based on the De Laval-Like Jet-Effect

Secondly, consider a case, when airfoil body 840 flies relativelyslowly, such that sliding sub-portions 853 pass cross-sectional areas868 with an M-velocity that remains lower than the specific M-velocity,i.e. M₈₅₃<M*, but high sufficient to provide that the increasedM-velocity of portion 856 is higher than M-velocity of sub-portions 853and reaches the specific M-velocity M*=√{square root over ((γ−1)/γ)} atthe critical condition point 864. In this case, M-velocity M₈₆₃ is thede Laval low velocity and the de Laval-like jet-effect is triggered,resulting in that the M-velocity of the divergent flow portion 857exceeds the specific M-velocity M*=√{square root over ((γ−1)/γ)}. Inthis case, the M-velocities M₈₆₁, M₈₆₃, M₈₆₄, M₈₆₅, and M₈₆₈ satisfy thefollowing conditions:

-   -   M₈₆₁<M₈₆₈<M*,    -   M₈₆₃<M₈₆₈<M*,    -   M₈₆₃<M₈₆₄=M*    -   M₈₆₁<M₈₆₄=M*, and    -   M₈₆₅>M₈₆₄=M*.        So, body 840 operates as a jet-booster basing on the de        Laval-like jet-effect occurring in the imaginary tunnel        downstream-behind airfoil body 840.

Thereby, the Coanda-jet-effect operation forcedly formsconvergent-divergent laminar-like streamlines downstream-behind airfoilbody 840, wherein the static pressure is distributed gradually along theconvergent-divergent laminar-like streamlines that provides an optimizedextension of air portion 857 resulting in the de Laval-like enhancedjet-effect accompanied by extra-cooling and extra-acceleration of airportion 857. This is one more teaching of the present invention.

A practical application of the phenomenon that, under certainconditions, outflowing portion 857 has an M-velocity higher than thespecific M-velocity is one of the primary teachings of the presentinvention.

It will be evident to a person skilled in the art that the enhancedjet-effect results in an optimized reactive thrust-force applied toairfoil body 840.

Thirdly, consider a case, when airfoil body 840's shape is optimizedusing the equation of principle (6.13), basing on an estimated linearsize of cross-section 868, and when airfoil body 840 flies with a deLaval low M-velocity M₈₅₁, i.e. lower than the specific M-velocityM*=√{square root over ((γ−1)/γ)}≈0.5345 Mach, but high sufficient toprovide that M-velocity of sliding sub-portions 853 reaches the value ofthe specific M-velocity, i.e. M₈₆₈=M* at the critical condition point868. Thereby, the enhanced de Laval-like jet-effect occursdownstream-behind the withers, providing that M*<M₈₅₄<M₈₅₅, where theindexes correspond to associated sliding air sub-portions. In this case,according to equation (6.13), shrinking portion 856, moving with a deLaval high M-velocity, is slowing down, becoming warmer and morecompressed, as moving on the way to the critical condition pointassociated with cross-section 864. The de Laval-like retarding-effectoccurs downstream-behind cross-section 864 resulting in portion 857expanding and further slowing down, warming, and compressing whilereaching cross-section 865. The M-velocities M₈₆₁, M₈₆₃, M₈₆₄, M₈₆₅, andM₈₆₈ satisfy the following conditions:

-   -   M₈₆₁<M₈₆₈ M*,    -   M₈₆₃>M₈₆₈ M*,    -   M₈₆₃>M₈₆₄ M*,    -   M₈₆₁<M₈₆₄=M*, and    -   M₈₆₅<M₈₆₄=M*.        So, in the final analysis, body 840 operates as a jet-booster,        triggering both the de Laval-like jet-effect and the de        Laval-like retarding-effect.

Fourthly, consider a case, when airfoil body 840's shape is optimizedusing the equation of principle (6.13), basing on an estimated linearsize of cross-section 868, and when airfoil body 840 flies with a deLaval high M-velocity, i.e. higher than the specific M-velocityM*=√{square root over ((γ−1)/γ)}≈0.5345 Mach. According to equation(6.13), the de Laval-like retarding-effect occurs in the imaginaryconvergent-divergent tunnel formed by streamlines 842. Namely, shrinkingair portions 852 are slowing down, becoming warmer and more compressed,as moving on the way to withers such that the M-velocity of thenarrowest sliding sub-portions 853 reaches the specific M-velocity, i.e.M₈₆₈=M* at the critical condition point 868; and further, portions 854continue to slow down while expanding downstream-behind the withers.Relatively slowly moving sliding sub-portions 855, now having a de Lavallow M-velocity, join downstream-behind cross-section 863, thereby,providing for resulting shrinking portion 856 acceleration, accompaniedby decrease of temperature and static pressure, while reaching again thespecific M-velocity M* at the narrowest cross-section 864. The deLaval-like jet-effect occurs downstream-behind cross-section 864resulting in expanding portion 857 further acceleration accompanied by adeeper decrease of temperature and static pressure on the way tocross-section 865. So, the M-velocities M₈₆₁, M₈₆₃, M₈₆₄, M₈₆₅, and M₈₆₈satisfy the following conditions:

-   -   M₈₆₁>M₈₆₈ M*,    -   M₈₆₃<M₈₆₈=M*,    -   M₈₆₃<M₈₆₄=M*,    -   M₈₆₁>M₈₆₄=M*, and    -   M₈₆₅>M₈₆₄=M*.        Again, in the final analysis, body 840 operates as a        jet-booster, triggering both the de Laval-like retarding-effect        and the de Laval-like jet-effect.

In view of the foregoing description referring to FIGS. 6a, 7a, 7b, 7c,8a and 8b , it will be evident to a person skilled in the art that:

-   -   a method for an airfoil body shape design, based on equation        (6.13) according to an exemplary embodiment of the present        invention, allows, modifying the overall geometry of the body,        to optimize efficiency of the enhanced jet-effect occurring        outside of the body;    -   the described convergent-divergent jet-nozzles can be applicable        to many apparatuses using mechanical and heat energy provided by        either a flowing gas or liquid;    -   triggering and controlling the desired de Laval-like jet-effect        can be provided by manipulating by the oncoming wind de Laval        M-velocity. As the M-velocity is temperature-dependent, one can        heat or cool air portions flowing within a specifically shaped        tunnel, in particular, in an imaginary tunnel around a flying        body;    -   reaching and controlling the desired de Laval-like jet-effect        can be provided by manipulating by the value of specific        M-velocity, depending on the generalized adiabatic        compressibility parameter γ. For example, one can inject a gas        composed of multi-atomic particles into a tunnel, in particular,        into an imaginary tunnel around a flying body. As well, it will        be evident to a person skilled in the art that, for example,        micro-flakes-of-snow could play a role of such multi-atomic        particles. Another technique to change the generalized adiabatic        compressibility parameter γ and thereby to control the specific        M-velocity is to ionize the flow, moving through the tunnel; and    -   the described convergent-divergent jet-nozzles can be applicable        to many apparatuses using mechanical and heat energy, provided        by flowing gas or liquid.

Two-Stage Operation of the Coanda-Jet-Effect

FIG. 8c is a schematic illustration of flying airfoil bodies 850 and860, arranged such that the withers of airfoil bodies 860 followdownstream-behind the withers of body 850. For simplicity and withoutloss of reasoning, each airfoil body 850 and 860 has the shape of anelongated drop 840 described above with reference to FIG. 8b . Allreference numerals 841, 861, 851, 862, 852, 868, 853, 842, and 854 arethe same as described referring to FIG. 8 b.

Consider a case, when flying airfoil bodies 850 and 860 meet oncomingportion 851 with a de Laval high M-velocity M₈₅₁, higher than thespecific M-velocity M*=√{square root over ((γ−1)/γ)}≈0.5345 Mach.According to equation (6.13), air sub-portions 852 are slowing down asconstricting on the way to the withers of body 850, such that M-velocityof the narrowest sliding sub-portions 853 reach the specific M-velocity,i.e. M₈₅₃=M* at the critical condition point 868. The de Laval-likeretarding-effect occurs downstream-behind the withers. It provides thecondition M*>M₈₅₄, where index “854” corresponds to air sub-portions854. So, airfoil bodies 860 meet oncoming sub-portions 854 flowingslower than with the specific M-velocity M*=√{square root over((γ−1)/γ)}, but high sufficient to provide the critical condition neartheir [bodies 860's] withers. Again, according to equation (6.13), airsub-portions 859 have an M-velocity M₈₅₉ higher than the specificM-velocity M*. Thus, flying airfoil bodies 850 and 860 meet the upstreamair portions, and leave the downstream air portions, flowing faster thanwith the specific M-velocity M*=√{square root over ((γ−1)/γ)}.Furthermore, a cumulative cross-section of air sub-portions 859, widerthan cross-section 861 of oncoming portion 851, means that theM-velocity M₈₅₉ is higher than the high M-velocity M₈₅₁ of oncomingportion 851. In this case, the Coanda-jet-effect two-stage operationaccelerates a portion of ambient airflow that originally moves fasterthan with the specific M-velocity M*. Thus, in contrast to the case whena body, having not-optimized shape, flies in air-environment withtransonic, and/or supersonic, and/or hypersonic velocities, flyingairfoil body 850, operating in tandem with each flying airfoil body 860,moving downstream behind the withers of airfoil body 850, results in aspecific effect of acceleration and cooling air portion 851, oncomingfaster than with the specific M-velocity M*. This is one other primaryteaching of the present invention.

FIG. 8d is a schematic drawing of a flying wing 870 having a two-humpedairfoil profile 871, constructed according to the principles of thepresent invention. The flying wing 870 comprises two withers: forward872 and rear 873, separated by concavity 874. The flying M-velocity ishigher than the specific M-velocity M*=√{square root over((γ−1)/γ)}≈0.5345 Mach.

An oncoming flow portion 875 runs at wing 870 and passes positions: 801,802, 803, 804, 805, 806, 807, 808, and 809 sequentially with associatedM-velocities: M₈₀₁, M₈₀₂, M₈₀₃, M₈₀₄, M₈₀₅, M₈₀₆, M₈₀₇, M₈₀₈, and M₈₀₉,correspondingly. The two-humped airfoil profile 871 provides for theCoanda-jet-effect two-stage operation: upstream-afore anddownstream-after concavity 874. At position 801, flow portion 875,having the de Laval high M-velocity M₈₀₁, is yet to be subjected to theCoanda-jet-effect operation over wing 870's profiled surfaces. Thetwo-humped airfoil profile 871 causes that the cross-sectional area ofportion 875 is varying as portion 875 moves over wing 870. So, portion875 shrinks at position 802 while upping over the forward part, has thefirst local minimum of cross-section area at position 803 above theforward withers 872, expands at position 804 while downing intoconcavity 874, reaches the local maximum of cross-section area atposition 805 when passing concavity 874, shrinks again at position 806on the way to the rear withers 873, gets the second local minimal valueof cross-section area at position 807 above the rear withers, andexpands at positions 808 and 809. According to equation (6.13), portion875 is subjected to the de Laval-like jet-effect and the de Laval-likeretarding-effect such that:

-   -   at position 802, the flow convergence is accompanied by the de        Laval-like retarding-effect resulting in compressing and warming        of flow portion 875 and a decrease of M-velocity, i.e.        M₈₀₁>M₈₀₂;    -   at position 803, the first critical condition point, where the        varying value of flow portion 875's cross-sectional area has the        first local minimum, provides for that the M-velocity of flow        portion 875 reaches the specific M-velocity M*, so,        M₈₀₁>M₈₀₂>M₈₀₃=M*, i.e. the critical condition of the de        Laval-like retarding-effect triggering is satisfied;    -   at position 804, the flow divergence is accompanied by further        compressing and warming of flow portion 875 and a decrease of        M-velocity lower than the specific M-velocity M*, i.e. M*>M₈₀₄;    -   at position 805 above concavity 874, the M-velocity M₈₀₅ is        minimal, thereby, providing the condition:        M ₈₀₁ >M ₈₀₂ >M ₈₀₃ =M*>M ₈₀₄ >M ₈₀₅;    -   at position 806, the flow convergence is accompanied by cooling        of flow portion 875, a decrease of static pressure, and an        increase of M-velocity, i.e. M₈₀₅<M₈₀₆;    -   at position 807, the second critical condition point, where the        varying value of the flow portion 875's cross-sectional area has        the second local minimum, is designed to provide for that the        M-velocity of flow portion 875 reaches the specific M-velocity        M*, i.e. the condition M₈₀₅<M₈₀₆<M₈₀₇=M* triggering the de        Laval-like jet-effect is satisfied; and so,    -   at positions 808 and 809, the flow divergence is accompanied by        further cooling of flow portion 875, a decrease of static        pressure, and an increase of M-velocity, i.e.        M₈₀₅<M₈₀₆<M₈₀₇=M<M₈₀₈<M₈₀₉.        Depending on profile 871, the M-velocity M₈₀₉ of flow portion        875 at downstream position 809, may exceed the high M-velocity        M₈₀₁ of flow portion 875 at upstream position 801, so, wing 870        may be used as a jet-booster based on the de Laval-like        jet-effect, operating at high velocities. In general, a use of a        two-humped airfoil profile of a wing flying with the de Laval        high M-velocities, in order to provide for the desired        jet-effect, is yet one of the teachings of the present        invention.

In view of the foregoing description referring to FIG. 8d , it will beevident to a person skilled in the art that the effect of highM-velocity acceleration by the Coanda-jet-effect two-stage operation isapplicable, for example, to a high-speed aircraft design.

In view of the foregoing description referring to FIGS. 6h, 7d, 8c, and8d , it will be evident to a person skilled in the art that, consideringa body, flying in air-environment with transonic, and/or supersonic,and/or hypersonic velocities, i.e. with high M-velocities higher thanthe specific M-velocity M*=√{square root over ((γ−1)/γ)},

-   -   in contrast to a case, wherein a body having an arbitrary shape        is decelerating when air-fluxes, which flow nearby around the        body, become warmer and extra-warmed,    -   a specifically-shaped body, having a two-humped airfoil profile        providing for the two-stage operation of the Coanda-jet-effect,        is accelerating, and air-fluxes, which flow nearby around the        accelerating specifically-shaped body, become cooled and        extra-cooled.

Cascaded Jet-Boosters

FIG. 9a is a schematic illustration of a sequential cascade of in-linearranged airfoil bodies 9011, 9013, 9014, 9015, and 9016, each in theshape of an elongated drop, exposed to oncoming wind 900 having theambient M-velocity substantially lower than the specific M-velocityM*=√{square root over ((γ−1)/γ)}. The shape of the elongated drops isoptimized using the equation of principle (6.13), basing on specifiedthickness of a boundary layer over convex withers, as describedhereinabove referring to FIGS. 8a and 8b . Points 9012 symbolize thatthe sequence of airfoil bodies may be much longer than shown. Forsimplicity, oncoming wind 900 is laminar. Trace a moving-small-portion910 of ambient oncoming wind 900 passing positions 911, 9110, 912, 913,9130, 914, 9140, 915, 9150, 916, 9160, and 917, considering a case whenmoving-small-portion 910 is subjected to the Coanda-jet-effect in anadiabatic process, defined by the partial pressure-“c” δP_(c), ratherthan affected by the skin-friction resistance, quantified by thedifference (a_(w)−a−δa). Moving-small-portion 910 at position 911 is yetto be subjected to the Coanda-jet-effect operation. I.e. at least theforward airfoil body 9011 meets moving-small-portion 910 withM-velocity, lower than the specific M-velocity M*=√{square root over((γ−1)/γ)}, and so body 9011 operates as a jet-booster based on theVenturi effect occurring in the adiabatic process in an imaginary tunneladjacent to body 9011, as described above with reference to FIG. 8b .Further, moving-small-portion 910 is subjected to a cascaded operationof the Coanda-jet-effect in the adiabatic process by in-line arrangedairfoil bodies 9011, 9013, 9014, 9015, and 9016, each of which operatesas an elemental jet-booster, while meeting moving-small-portion 910 withM-velocity, lower than the specific M-velocity M*=√{square root over((γ−1)/γ)}. The cascaded operation of the Coanda-jet-effect results inaligning of the Brownian random motion of moving-small-portion 910'smolecules with the surfaces of in-line arranged airfoil bodies 9011,9013, 9014, 9015, and 9016, that is observed as an increase of theeffective velocity of moving-small-portion 910, accompanied bymoving-small-portion 910 temperature decrease, as moving-small-portion910 sequentially passes positions 9110, 9130, 9140, 9150, and 9160,where flowing as ambient-adjoining convergent-divergent jetstreams.Thus, this results in an increase of moving-small-portion 910's kineticenergy at the expense of moving-small-portion 910's internal heatenergy. Consider certain identical cross-sectional areas at positions911, 912, 913, 914, 915, 916, and 917, marked by dashed ellipses, suchthat the Coanda-jet-effect operation influence is still perceptiblewithin the marked areas. Considering flow velocities much lower than thespecific M-velocity M*=√{square root over ((γ−1)/γ)}, the effectivevelocity of flow crossing the marked areas at positions 911, 912, 913,914, 915, 916, and 917 increases exponentially as the flow moves alongthe sequential cascade of in-line arranged airfoil bodies 9011-9016. Forexample, if the Coanda-jet-effect operation of each of airfoil bodies9011-9016 in the adiabatic process provides an increase of the effectivevelocity of a flow portion, crossing the associated marked area, on 2%,then after 35 airfoil bodies 9011-9016 the effective velocity of thewind portion, crossing the marked area, is twice as high as the velocityof oncoming wind 900 yet to be subjected to the Coanda-jet-effectmulti-stage cascaded operation. Consider a case, when the M-velocityM₉₁₃₀ of moving-small-portion 910, flowing as an ambient-adjoiningconvergent-divergent jetstream nearby the withers of airfoil body 9013,reaches the specific M-velocity M*=√{square root over ((γ−1)/γ)} atposition 9130. Triggering of the de Laval-like jet-effect causes theM-velocity M₉₁₄ at position 914 to become higher than the specificM-velocity M*. The moving-small-portion 910 becomes cooled betweenpositions 913 and 9130 and becomes extra-cooled between positions 9130and 914. Running at airfoil body 9014, moving-small-portion 910 issubjected to the de Laval-like retarding-effect, such that the portion'sM-velocity decreases down to the specific M-velocity M*=√{square rootover ((γ−1)/γ)} at position 9140 nearby the withers of airfoil body9014, and becomes lower than the specific M-velocity LM at position 915.The moving-small-portion 910 becomes warmer between positions 914 and9140 and becomes extra-warmed between positions 9140 and 915. Thenmoving-small-portion 910 is subjected to the de Laval-like jet-effectand the M-velocity increases again. Thus, when the sequence of airfoilbodies 9011-9016 is sufficiently long, the effective M-velocity ofmoving-small-portion 910 reaches the value of the specific M-velocityM*=√{square root over ((γ−1)/γ)} nearby the withers of airfoil bodiesand varies around the value between the airfoil bodies. This is yet onemore of the teachings of the present invention.

In view of the foregoing description referring to FIG. 9a , it will beevident to a person skilled in the art that:

-   -   in a more general case, when oncoming wind 900 is turbulent,        such that moving-small-portion 910 comprises whirling groups of        molecules, the Coanda-jet-effect multi-stage cascaded operation        results in aligning also of the turbulent motion of the whirling        groups of molecules with the surfaces of in-line arranged        airfoil bodies 9011, 9013, 9014, 9015, and 9016, that is        observed as an increase of the effective velocity of        moving-small-portion 910, accompanied by moving-small-portion        910's inner turbulence decrease, as moving-small-portion 910,        flowing as ambient-adjoining convergent-divergent jetstreams        nearby around the withers of airfoil bodies 9011, 9013, 9014,        9015, and 9016, sequentially passes positions 9110, 9130, 9140,        9150, and 9160, correspondingly. Thus, this results in an        increase of moving-small-portion 910's kinetic energy also at        the expense of moving-small-portion 910's inner turbulent        energy;    -   the effect of M-velocity acceleration and stabilization by a        multi-stage cascaded operation of the Coanda-jet-effect thereby        reinforced multi-repeatedly is applicable, for example, to a        high-speed long-train design;    -   the effect of M-velocity stabilization is applicable, for        example, to a flying train-like object, in particular, supplied        with wings, which are not shown here, providing for a        lift-force; an arrangement of airfoil bodies 9011, 9013, 9014,        9015, and 9016 along a smoothly curved locus, instead of the        in-line arrangement, can be implemented; and    -   the stabilized temperature difference between the extra-cooled        airflow portions subjected to the triggered de Laval-like        jet-effect and the extra-warmed airflow portions subjected to        the triggered de Laval-like retarding-effect may be used to        power a Peltier-element operating as a thermoelectric generator        producing electricity.

Reference is now made again to prior art FIG. 9a , wherein now, all thein-line arranged airfoil bodies 9011, 9013, 9014, 9015, and 9016 aremade from a conductive material, for simplicity, from a hypotheticsuper-conductor, wherein the sequence is exposed to electric flux 900.In view of the foregoing description referring to FIG. 1f , the inventorpoints out that the effective electric flux crossing the marked areas atpositions 911, 912, 913, 914, 915, 916, and 917 is self-increasingexponentially as flowing along the sequential cascade of in-linearranged airfoil conductive bodies 9011-9016 due to the electromagneticjet-effect.

FIG. 9b is a schematic illustration of a sequential multi-stage cascadeof outer and nested airfoil rings 920, exposed to oncoming wind 921.Outer and nested airfoil rings 920 are formed by coiled-up walls havingan actually-airfoil wing profile, similar, for example, to the profileof actually-airfoil wing 810, shown schematically in FIG. 8a . Thereby,outer and nested airfoil rings 920 have shapes of streamlined convergingnozzles. The actually-airfoil wing profiles are optimized using theequation of principle (6.13), basing on specified thickness of aboundary layer over convex withers, as described hereinabove with thereferences to FIG. 8a . Points 929 symbolize that the sequence of outerand nested airfoil rings 920 may be much longer than shown. Airflowportions 922, flowing as ambient-adjoining convergent-divergentjetstreams, sliding outside of the sequential multi-stage cascade ofouter rings 920, as well as wind portions 923, flowing and impactinginside of outer and nested airfoil rings 920, are subjected to theCoanda-jet-effect operation. Again, consider a case when airflowportions 922 and 923 are subjected to the Coanda-effect operation ratherthan to skin-friction resistance, thereby providing that each pair ofouter and nested airfoil rings 920 operates as an elemental jet-booster.Airflow portions 922 and 923 join a cumulative outflow 924, wherein theCoanda-effect provides streamlines 925 forming an imaginaryconvergent-divergent nozzle downstream-behind the sequential multi-stagecascade of outer and nested airfoil rings 920. A sufficiently longmulti-stage cascade of outer and nested airfoil rings 920 provides thatthe M-velocity of resulting cumulative outflow 924 reaches the specificM-velocity M*=√{square root over ((γ−1)/γ)} at the minimal cross-section926 of the imaginary convergent-divergent nozzle and the de Laval-likejet-effect is triggered downstream-behind the minimal cross-section 926.Airflow portion 927 is expanded adiabatically; therefore, it isextra-cooled and extra-accelerated.

A prolonged multi-stage cascade of outer and nested airfoil rings 920may enable the M-velocity of airflow portions 922 to reach the specificM-velocity M* nearby the withers of airfoil outer rings 920. In thiscase, airflow portions 922 become subjected to the de Laval-likejet-effect, such that the effective M-velocity of airflow portions 922is stabilized, as described hereinbefore with reference to FIG. 9a ,considering a sequential multi-stage cascade of in-line arranged airfoilbodies, each having the shape of an elongated drop.

FIG. 9c is a schematic illustration of a modified sequential multi-stagecascade of the outer and nested airfoil rings 920 of FIG. 9b into a pairof unbroken spirals shaped as the Archimedean screws 931 and 932 byhelical coiling-up walls having airfoil profile 937, for example,similar to described above with reference to FIG. 8a . Airfoil profile937, also shown separately above and to the left in an enlarged scale,is optimized using the equation of principle (6.13), basing on specifiedthickness of a boundary layer over convex withers, as describedhereinabove with the reference to FIG. 8a . Oncoming airflow portion 933is yet to be subjected to the Coanda-jet-effect operation. Both: thesliding outside air sub-portions 934 flowing around and the insideimpacting air sub-portions 935 flowing through the pair of spirals 931and 932, are subjected to the Coanda-jet-effect operation, resulting ina converging flow when convergent flow sub-portions 934 and 935laminarly join a resulting cumulative outflow 936. I.e. a fragment [forinstance, one coil] of the pair of spirals 931 and 932 operates as anelemental jet-booster, and a longer fragment of converging spirals 931and 932 provides higher acceleration of the airflow. Again, theCoanda-jet-effect provides streamlines 930 forming an imaginaryconvergent-divergent jet-nozzle downstream-behind the airfoilconstruction.

Moreover, the two spirals 931 and 932 have opposite helical screwingrotations, namely: clockwise and inverse-clockwise, thereby providing avariable cross-sectional area of gaps between the walls of the twospirals 931 and 932. The variable cross-sectional area of the gapsprovides a Venturi effect for velocities lower than the specificM-velocity M*=√{square root over ((γ−1)/γ)} and the de Laval-likejet-effect for velocities providing for reaching the specific M-velocityM*=√{square root over ((γ−1)/γ)} at the critical condition point wherethe variable cross-sectional area of gaps becomes minimal. Sufficientlylong converging spirals 931 and 932 provide acceleration of the airflowand stabilization of the effective velocity at the value of the specificM-velocity M*=√{square root over ((γ−1)/γ)} analogous to the casesdescribed above with references to FIGS. 9a and 9 b.

In view of the foregoing description of FIGS. 9a, 9b, and 9c , it willbe evident to a person skilled in the art that:

-   -   One can implement many alterations, re-combinations and        modifications of elemental jet-boosters, taught herein, without        departing from the spirit of the disclosure that can be        generalized as the following. A sufficiently long aggregation of        elemental jet-boosters provides acceleration of an airflow        portion, reaching the specific M-velocity M*=√{square root over        ((γ−1)/γ)}, thereby triggering alternating the de Laval-like        jet-effect and the de Laval-like retarding-effect, resulting in        a stable alternation of the airflow portion effective M-velocity        above and below the specific M-velocity M*=√{square root over        ((γ−1)/γ)} between the elemental jet-boosters;    -   and    -   The cumulative useful kinetic-power, including both: the        originally brought kinetic-power and the acquired kinetic-power,        provided by a multiplicity of elemental jet-boosters, aggregated        into an adiabatic converging system, depends on a quality and        quantity of the elemental jet-boosters and how the elemental        jet-boosters are arranged and exploited. Moreover, it will be        evident to a person skilled in the art that a sequential in-line        multi-stage cascading of the elemental jet-boosters has an        especial sense.

For example, consider an aggregation comprising N elemental jet-boostersexposed to an ambient flow and oriented such that each elementaljet-booster provides an increase of the effective velocity of the flowportion moving through a certain effective cross-sectional area, by afactor F, wherein F>1, and for simplicity and without loss of theexplanation generality, consider a case of sufficiently low velocity ofthe ambient flow and assume that it is the same factor, independently ofthe elemental jet-boosters arrangement and exploitation. As well, forsimplicity, consider the case, when the M-velocities of accelerated flowremain lower than the specific M-velocity M*=√{square root over((γ−1)/γ)}, thereby, justifying neglecting the flow density change infurther approximate estimations. As the kinetic-power of a flow portionmoving through a certain cross-sectional area is directly-proportionalto the cross-sectional area and proportional to the third power of theflow portion velocity, each elemental jet-booster, when operatingseparately, launches a jetstream having the solitary usefulkinetic-power, indicated by W₁, proportional to the third power of thefactor F, expressed by W₁=W₀×F³, where W₀ is the originally broughtambient useful kinetic-power associated with the effectivecross-sectional area of one elemental jet-booster.

The solitary acquired kinetic-power ΔW₁ is defined by the differencebetween the solitary useful kinetic-power W₁ and the originally broughtambient useful kinetic-power W₀, namely, ΔW₁=W₀×(F³−1).

The aggregation, comprising N such elemental jet-boosters and therebyaccelerating the flow portions, moving through N effectivecross-sectional areas, results in the cumulative useful kinetic-power:

-   -   indicated by W_(parallel), equal to W_(parallel)=N×W₁=N×W₀×F³,        wherein the cumulatively acquired kinetic-power ΔW_(parallel) is        defined as:        ΔW _(parallel) =N×ΔW ₁ =N×W ₀×(F ³−1),    -   in the case, when the elemental jet-boosters operate        independently, that occurs,        -   if the elemental jet-boosters are arranged in parallel, or        -   if the elemental jet-boosters are arranged sequentially, but            operating in a not adiabatic process, allowing for the            solitary useful kinetic-power W₁ to be consumed in parallel            within or behind each elemental jet-booster and restored            afore each next elemental jet-booster;    -   or, alternatively,    -   indicated by W_(sequential), equal to        W_(sequential)=W₀×(F³)^(N), wherein the cumulatively acquired        kinetic-power ΔW_(sequential) is defined as:        ΔW _(sequential) =W ₀×[(F ³)^(N) −N],    -   in the case, when the elemental jet-boosters are arranged        sequentially operating in the adiabatic process, and the        consumption of the cumulative useful kinetic-power is allowed        behind the downstream-end of the last elemental jet-booster        only.        In an exemplary practical case, the effective velocity increase        factor equals F=1.097. Then the following conditions become        satisfied:    -   the condition W_(sequential)<W_(parallel) is satisfied for N≤8;    -   the condition W_(sequential)>W_(parallel) is satisfied for N≥9;    -   the condition W_(sequential)>2W_(parallel) is satisfied for        N≥13;    -   the condition W_(sequential)>3W_(parallel) is satisfied for        N≥15; and    -   the condition W_(sequential)>4W_(parallel) is satisfied for        N≥16.

In view of the foregoing description of FIGS. 9a, 9b, and 9c , one ofthe primary teachings is that an artificial wind can be used for aprofitable harvesting of electricity. For example, one can:

-   -   use a big-front ventilator [or group of ventilators], having        50%-net-efficiency, i.e. consuming electric-power W_(consumed)        and creating an originally incoming artificial airflow, bringing        kinetic-power W_(income)=0.5×W_(consumed), wherein the        originally incoming artificial airflow has the front area        A_(income) of 4 times bigger than the effective cross-sectional        area of an elemental jet-booster and has the effective velocity        u_(income);    -   implement a sequential multi-stage cascade, comprising N=15        elemental jet-boosters, each of which is characterized by the        effective velocity increase factor F=1.097, such that altogether        making an outflowing artificial jetstream, having velocity        u_(jetstream)=u_(income)×F^(N) [F^(N)=1.097¹⁵≈4] and having the        resulting effective front cross-sectional area A_(jetstream),        decreased approximately 4 times relative to the area A_(income)        of originally incoming airflow        [A_(income)/A_(jetstream)=F^(N)≈4]. Thus, the outflowing        artificial jetstream brings the resulting useful kinetic-power        W_(jetstream), estimated as:        W_(jetstream)=[(u_(jetstream)/u_(income))×(A_(jetstream)/A_(income))]×W_(income),        i.e.        W_(jetstream)=[4³/4]×W_(income)=[16]×0.5×W_(consumed)=8×W_(consumed);        and    -   use a wind-turbine, producing electricity with        50%-net-efficiency, thereby, harvesting the useful        electric-power W_(useful) of 4 times higher than the consumed        electric-power W_(consumed), namely, W_(useful)        0.5×W_(jetstream)=0.5×(8×W_(consumed))=4×W_(consumed).        Wherein, the profit becomes greater than estimated, when the de        Laval-like jet-effect is triggered. Thereby, in view of the        foregoing description referring to FIGS. 9a, 9b, and 9c , it        will be evident to a person skilled in the art that a profitable        harvesting of electricity, using a jet-effect created by a        multi-stage cascaded operation of the Coanda-jet-effect thereby        reinforced multi-repeatedly, is feasible, for example, attaching        sequentially arranged elemental jet-boosters to a        sufficiently-long moving vehicle and using a wind-turbine,        arranged behind the downstream-end of the last elemental        jet-booster.

In view of the foregoing description referring to FIGS. 9a, 9b, and 9c ,the inventor points out that, when reaching the stabilized effectivevelocity equal to the value of the specific M-velocity M*=√{square rootover ((γ−1)/γ)}, the periodical local extra-acceleration andextra-retarding generate a forced extra-intensive elemental acousticwave, wherein the distance between each two neighbor withers equals ahalf of wavelength of the forced extra-intensive elemental acousticwave. Furthermore, the forced extra-intensive elemental acoustic wavesare superposed in-phase thereby constituting the resultingextra-intensive acoustic wave as constructive interference. It will beevident to a person skilled in the art that the arrangement of airfoilbodies, either:

-   -   9011, 9013, 9014, 9015, and 9016 as shown in FIG. 9a ; or    -   a sequential multi-stage cascade of outer and nested airfoil        rings 920 as shown in FIG. 9b ; or    -   a pair of unbroken spirals shaped as the Archimedean screws 931        and 932 by helical coiling-up walls having airfoil profile 937,        as shown in FIG. 9 c,        subjected to the generalized jet-effect (namely, the        Coanda-jet-effect, the de Laval-like jet-effect, the de        Laval-like retarding effect, and the enhanced waving jet-effect)        and supplied by an acoustic detector capable of detection of the        resulting extra-intensive acoustic wave power, can play a role        of an electricity generator that, in the final analysis,        produces the electrical power at the expense of the warmth of        the air.        Kinetic Energy Accumulation, Conservation, and Use

FIG. 9d illustrates schematically a circulating system 940 comprising amulti-stage cascade of many [8 shown] airfoil bodies 941 submerged in afluid and arranged circumferentially. The rotation is in theinverse-clockwise direction as indicated by curved arrow 942.

For simplicity, the shape and multi-stage cascading of airfoil bodies941 are similar to the shape and multi-stage cascading of airfoil bodies9011-9016 described above with reference to FIG. 9a , but now anasymmetry of shapes and attack angles of airfoil bodies 941 are suchthat the trajectories of flowing fluid portions 944 are aligned with theassociated arc of circling.

The fluid sub-portions 943, flowing around airfoil bodies 941, aresubjected to the Coanda-effect and skin-friction; wherein when flowingadjacent to the withers of airfoil bodies 941, fluid sub-portions 943are subjected to a cross-sectional varying, performing ambient-adjoiningconvergent-divergent jetstreams. Consider a case, when flowing fluidsub-portions 943 are subjected to the Coanda-effect operation ratherthan affected by the skin-friction resistance, and are, thereby,accelerated in the clockwise direction, forming flowing fluid portions944 between circulating airfoil bodies 941. I.e. airfoil bodies 941operate as elemental jet-boosters, analogous to the operation of airfoilbodies 9011-9016 (FIG. 9a ).

The sequential operation of the Coanda-jet-effect results in fluidportion 944's velocity distribution within cross-sections 9440, whereinthe distribution occurs at the expense of fluid portion 944'stemperature decrease. The term “local velocity” refers to the velocityof a flowing fluid sub-portion relative to the nearest flying body 941.The local velocity is directed substantially along a local sagittalaxis, associated with the nearest flying body 941.

The circulation creates a positive feedback loop, providing a cyclingoperation of the Coanda-jet-effect within an imaginary toroidal spacehaving cross-sections 9440. The cycling operation of theCoanda-jet-effect results in further aligning of the Brownian randommotion of fluid sub-portions 943 molecules with the profiles of airfoilbodies 941 that is observed as a further increase of the effective localvelocity of circulating fluid sub-portions 943, accompanied by the fluidsub-portions 943 temperature further decrease. This provides furtherdistribution of portions 944 local velocity and further acceleration offlowing fluid sub-portions 943 up to reaching the specific M-velocityM*=√{square root over ((γ−1)/γ)} in the narrowest cross-section near thewithers. The reaching of the specific M-velocity M*=√{square root over((γ−1)/γ)} triggers alternating both the de Laval-like jet-effect andthe de Laval-like retarding-effect, similar to that describedhereinbefore with reference to FIG. 9a . Thus, the M-velocities ofsub-portions 943 become stabilized at the specific M-velocityM*=√{square root over ((γ−1)/γ)}, and M-velocities of flowing portions944 alternate above and below the specific M-velocity M*=√{square rootover ((γ−1)/γ)}. Thus, the stabilized circulation of portions 944 withinthe imaginary toroidal space, having cross-sections 9440, may beinterpreted as a conservation of the flowing portions 944 kinetic energywithin the imaginary toroidal space. The accumulated and conservedkinetic energy of flow, indicated by K_(acc), is equal toK_(acc)=0.5ρ_(eff)V_(tor)u_(eff) ², where ρ_(eff) is the effectivedensity of circulating fluid, V_(tor) is the volume of the imaginarytoroidal space, and u_(eff) is the effective local velocity of thecirculating fluid, equal to u_(eff)=M*×u_(sound), where u_(sound) is thespeed of sound in the fluid.

In view of the foregoing description of FIG. 9d , it will be evident toa person skilled in the art that:

-   -   a part of the accumulated kinetic energy K_(acc) of flow can be        consumed, for instance, in the form of a jetstream, outflowing        from the imaginary toroidal space, that is not shown here; and    -   an arisen lack of the consumed kinetic energy of flow can be        accumulated again up to the value K_(acc) by sucking fresh        portions of the surrounding fluid into the imaginary toroidal        space.        In view of the foregoing description of FIG. 9d , it will be        evident to a person skilled in the art that:    -   circulating multi-stage cascade 940 operates similarly to a long        in-line multi-stage cascade of many airfoil bodies 9011-9016        described hereinbefore with reference to FIGS. 9a, 9b, and 9c ,        but now fluid portions 944 move along a curved and closed        trajectory. Such an implementation of inverse circulation of        flow relative to the direction of bodies 941 s′ rotation is one        of the teachings of the present invention as well;    -   a fluid portion, circulating within the imaginary toroidal space        and having the local velocity, static pressure, temperature, and        density substantially distributed in cross-sections 9440, is        subjected to inter-diffusion with the contacting fluid portion        remained out of the imaginary toroidal space that results, in        particular, in a caloric exchange between the fluid portions;        and    -   a circulating multi-stage cascade of elemental jet-boosters may        function as a self-rotating warmth-to-motion engine.

FIG. 9e is a schematic top-view of a stationary circumferentialarrangement of many [42 shown] elemental jet-boosters 950, therebyembodying a vortex-generator, constructed according to the principles ofthe present invention and exposed to natural ambient wind 951, bringingfresh air portions storing both:

-   -   the kinetic energy of flow [i.e. the kinetic energy the        directional laminar motion, or, in terms of the kinetic theory        of gas, the kinetic energy of the air molecules headway motion];    -   the kinetic energy of the Brownian random motion of air        molecules [i.e. the inner heat]; and, in a more general case,    -   the kinetic energy of whirling groups of air molecules [i.e. the        turbulent energy].

The center of the circle is marked by point 957. The elementaljet-boosters 950 have an effective height 9571 and the circumferentialarrangement occupies a circle having effective overall diameter 9572.So, the circumferential arrangement overall shape is an imaginarycylinder having a base of effective overall diameter 9572 and a side ofheight 9571.

For simplicity, the shown shape and multi-stage cascading of elementaljet-boosters 950 are similar to the shape and multi-stage cascading ofairfoil outer and nested airfoil rings 920 described hereinbefore withreference to FIG. 9b . The airflow portions 953, flowing through theinner space of elemental jet-boosters 950, and portions 955 and 956flowing as ambient-adjoining convergent-divergent jetstreams nearbyaround elemental jet-boosters 950, are subjected to theCoanda-jet-effect operation and, thereby converge. The circumferentialarrangement provides that some elemental jet-boosters 950 are orientedto natural ambient wind 951, such that they operate asconverging-nozzles; and some other elemental jet-boosters 950 areoriented to natural ambient wind 951, such that they operate asdivergent nozzles. This asymmetry of elemental jet-boosters 950orientations causes the oncoming airflow front to be non-uniform indirection and therefore has a tendency to flow around a side of thearrangement, as schematically shown by arrows 952. Considering flowM-velocities much lower than the specific M-velocity M*=√{square rootover ((γ−1)/γ)}, the multiplicity of elemental jet-boosters 950 causesaccelerated wind sub-portions at position 954 to have local velocities,substantially higher than the velocity of natural ambient wind 951. Thisresults in a circulation of airflow portions 953, 955, and 956 within animaginary toroidal space, having effective overall diameter 9572 and across-section, marked by dashed ellipse 9573 having a diametercorresponding to effective height 9571. Circulating airflow portions953, 955, and 956, become subjected to the Coanda-jet-effect circulatingoperation in a positive feedback loop, resulting in further aligning ofthe Brownian random motion of air molecules with the airfoil surfaces ofelemental jet-boosters 950 that is observed as an increase of theeffective local velocity of circulating airflow portions 953, 955, and956, accompanied by the airflow portions temperature decrease. In a moregeneral case, when airflow portions 953, 955, and 956 have innerturbulence, i.e. airflow portions 953, 955 and 956 comprise whirlinggroups of molecules, the Coanda-jet-effect multi-stage cascadedoperation results in aligning also of the turbulent motion of thewhirling groups of molecules with the airfoil surfaces of elementaljet-boosters 950, that is observed as an increase of the effective localvelocity of airflow portions 953, 955, and 956, accompanied by theairflow portions inner turbulence decrease, as the airflow portions movewithin the imaginary toroid, sequentially passing elemental jet-boosters950. Thus, this results in an increase of airflow portions 953, 955, and956 kinetic energy also at the expense of airflow portions 953, 955, and956 inner turbulent energy. The effective local velocity increasecontinues until reaching the specific M-velocity M*=√{square root over((γ−1)/γ)}. Then the effective local velocity is stabilized triggeringalternating both the de Laval-like jet-effect and the de Laval-likeretarding-effect, as described hereinbefore with references to FIGS. 9aand 9d . In particular, an even number of jet-boosters 950 provides thatthe circulating airflow local velocities become steady-statelydistributed in space. The circulating portions become cooled andextra-cooled, where the de Laval-like jet-effect is triggered, andbecome warmer and extra-warmed, where the de Laval-like retarding-effectis triggered.

In view of the foregoing description of FIG. 9e , and referring to thedescription of FIG. 4, it will be evident to a person skilled in the artthat:

-   -   Airflow portions 953, 955, and 956, circulating within the        imaginary toroidal space and having the local velocity, static        pressure, temperature, and density substantially distributed in        cross-sections 9573, are subjected to inter-diffusion with the        contacting airflow portions remained out of the imaginary        toroidal space. This results, in particular, in the caloric        exchange between the airflow portions;    -   The circumferential arrangement of many elemental jet-boosters        950 exposed to the natural ambient wind may function as a        warmth-to-vortex/tornado generator that can power a rotor of an        electricity generator;    -   The circumferential arrangement of many elemental jet-boosters        950 exposed to the natural ambient wind accumulates and        conserves the kinetic energy of flow K_(acc) independently of        the direction of horizontal wind, as well as independently of        any variation in the natural gusty wind direction, and        furthermore, independently of any variation of the natural gusty        wind non-zero velocity;    -   The stabilized temperature difference between the extra-cooled        airflow portions, subjected to the triggered de Laval-like        jet-effect, and the extra-warmed airflow portions, subjected to        the triggered de Laval-like retarding-effect, may be used to        power a Peltier-element operating as thermoelectric generator        producing electricity, while the consumed heat power is        restoring at the expense of the surrounding air caloric entering        the imaginary toroidal space;    -   The circumferential arrangement of many converging airfoil        bodies operating as elemental jet-boosters 950 exposed to        natural ambient humid wind can be used, for example, as an air        cooler triggering condensation of water-vapor into water-drops        that can be applied to water harvesting from humid air.        Furthermore, it will be evident to a person skilled in the art        that the condensation of water-vapor into water-drops is an        exothermic process resulting in that the stabilized circulation        of airflow has the stabilized temperature defined by the        so-called “dew-point temperature” corresponding to the humidity        of ambient wind; thus, the area, bordered by the        circumferentially arranged elemental jet-boosters, performs an        oasis of a stably-eddying windiness and refreshing coolness; and    -   In a more general case, the circumferential arrangement of many        converging airfoil bodies, operating as elemental jet-boosters        950 exposed to natural ambient wind 951, can enable rotations        around the vertical axis through point 957 and power a rotor of        an electricity generator. Alternatively, different arrangements        of wind-turbines can be adapted to use the fast rotations of        wind portions, again, while the consumed heat-power is restoring        at the expense of the surrounding air caloric entering the        imaginary toroidal space.

In view of the foregoing description referring to FIGS. 9a, 9b, 9c, 9d,and 9e , it will be evident to a person skilled in the art that:

-   -   one can configure many modifications of airfoil bodies operating        as elemental jet-boosters, providing flow acceleration due to a        multi-stage cascaded operation of the Coanda-jet-effect to reach        the specific M-velocity M*=√{square root over ((γ−1)/γ)} and,        thereby, to trigger the de Laval-like jet-effect arising; and    -   one can configure many modifications of elemental jet-boosters        arrangements along smoothly curved loci, instead of the        circumferential arrangement. The arrangement locus can be at        least one of a line, an arc, a spiral of Archimedes, an outer        helical outline of the Archimedean screw, a rounded contour, an        ellipse, and a circumference.

FIG. 9f is a schematic top-view of an adiabatic aerodynamic system 960,constructed according to the principles of the present invention,comprising:

-   -   the stationary circumferential arrangement of many elemental        jet-boosters 950, described above with reference to FIG. 9e        having the same reference numerals 951, 952, 953, 954, 955, 956,        957, 9571, 9572, and 9573; and    -   stationary airfoil wings 958, arranged within the mentioned        imaginary cylinder having the basis of effective overall        diameter 9572 and the side of height 9571.

Airflow portions 959 are entrapped and drawn by stably circulatingadjacent airflow portions 956, and so are stable-circulating as well.

In one application, stationary airfoil wings 958 are configured andoriented to originate lift-forces under the influence ofstable-circulating airflow portions 959.

Alternatively, the airfoil wings 958 have symmetrical airfoil shaperelative to a horizontal plane, and thereby do not originatelift-forces, but result in reactive thrust-forces directed along localsagittal axes, associated with nearest airfoil wings 958, due to thejet-effect as described hereinbefore referring to FIG. 8b , therebyenabling airfoil wings 958 rotations around the vertical axis throughpoint 957. Wherein, if airflow portions 959 are subjected to theCoanda-effect operation rather than affected by the skin-frictionresistance, then airfoil wings 958 rotation is in the inverse-clockwisedirection, i.e. against the direction of airflow portions 959 rotation.This phenomenon is one of the teachings of the present invention aswell.

In view of the foregoing description referring to FIG. 9f , it will beevident to a person skilled in the art that the lift-force, acting onwings 958, is independent of the direction of horizontal natural ambientwind 951, as well as independent of any variation in the natural gustywind direction, and furthermore, independent of any variation of thenatural gusty wind non-zero velocity; and it will be evident to a personskilled in the art that the lift-force, acting on wings, can becontrolled by the airfoil wings configuration, arrangement, andorientation. An implementation of an adiabatic aerodynamic system,having no moving parts and providing for a stable and predictablelift-force generated at the expense of ambient air heat energy, is alsoone of the teachings of the present invention.

In view of the foregoing description referring to FIGS. 9e and 9f , itwill be evident to a person skilled in the art that, implementing anadiabatic aerodynamic system comprising a circumferential arrangement ofmany elemental jet-boosters, either a wide-front fluid flow or manyfluid jetstreams, made artificially, can be used instead of the naturalambient wind.

In view of the foregoing description referring to FIG. 9f , it will beevident to a person skilled in the art that the principles, applied tothe construction of adiabatic aerodynamic system 960, allow for a designof a flying-saucer. Wherein, in contrast to a principle of helicopter,where rotating wing-like blades interact with stationary air, here,stationary wings 958 interact with rotating airflow portions 959. Aswell, to provide a controlled maneuvering, adiabatic aerodynamic system960 can be supplied with airfoil blades, similar to stationary wings958, but having controllable degrees of freedom to be orientedasymmetrically relative to point 957, thereby, redirecting the stablycirculating airflow portions out of the adiabatic aerodynamic system andallowing for a reactive push in any desired direction, as well as forstabilizing the flying-saucer position in atmosphere. Furthermore, inview of the foregoing description referring to FIG. 9f , it will beevident to a person skilled in the art that the energy, conserved in theform of the stable-circulating airflow portions kinetic energy, allowsfor a fast maneuvering of the flying-saucer.

In view of the foregoing description referring to FIG. 9f , it will beevident to a person skilled in the art that adiabatic aerodynamic system960, exposed to natural humid wind, can be adapted for the humiditycondensation, and thereby, water harvesting from humid air. To estimatean efficiency of the water condensation, consider a stationarycircumferential arrangement of many elemental jet-boosters 950 exposedto natural ambient humid wind moving with velocity, indicated by u₅₅₁u₉₅₁, and characterized by parameters of static pressure P₉₅₁,temperature T₉₅₁, density ρ₉₅₁, and relative humidity h₉₅₁, wherein in anormal exemplary case, the parameters are quantified as: u₉₅₁=10 m/sec,P₉₅₁=100 kPa, T₉₅₁=298 K, ρ₉₅₁=1.2 kg/m³, and h₉₅₁=60%. The values ofP₉₅₁, T₉₅₁, ρ₉₅₁, and h₉₅₁, correspond to absolute humidity H₉₅₁=14 g/m³and so-called “dew-point temperature”, equal to T_(dew)=289K for thecase. Consider an exemplary implementable case, when the effectiveoverall diameter 9572 is equal to D₉₅₇₂=20.3 m, and the stabilized airmotion with effective M-velocity, indicated by M₉₅₇₃, equal to thespecific M-velocity M*=√{square root over ((γ−1)/γ)}, is throughcross-sections 9573, having the effective diameter, indicated by d₉₅₇₃,equal to 0.5m. The volume of the imaginary toroidal space, having theeffective overall diameter D₉₅₇₂ and the cross-sectional diameter d₉₅₇₃,is equal to V_(tor)=π×D₉₅₇₂×0.25π×d₉₅₇₃≈12.5 m³, and the imaginarytoroidal space bordering area, indicated by A_(tor), is equal toA_(tor)=πD₉₅₇₂×πd₉₅₇₃≈100 m². The imaginary toroidal space volumeV_(tor) comprises potentially yet to be condensed water-vapor, havingmass M_(V), equal to M_(V)=V_(tor)H₉₅₁≈175 g. The acquired kineticenergy of the circulating airflow, K_(acquired), is defined asK_(acquired)=0.5×V_(tor) [ρ_(eff)u_(eff) ²−ρ₉₅₁u₉₅₁ ²], where theeffective local velocity u_(eff) of the airflow, circulating within theimaginary toroidal space, is quantified as u_(eff)=M₉₅₇₃×u_(sound)≈184m/sec, and the effective density ρ_(eff) interrelates with thestabilized dew-point temperature T_(dew), according to theClapeyron-Mendeleev gas state law for an adiabatic process. Namely,

$\rho_{eff} = {{\rho_{951}\left( \frac{T_{dew}}{T_{951}} \right)}^{\frac{1}{\gamma - 1}} \approx {1.2 \times \left( \frac{289}{298} \right)^{2.5}} \approx {1.1\mspace{14mu}{kg}\text{/}m^{3}}}$Thereby, the acquired kinetic energy K_(acquired), is estimatedapproximately asK _(acquired)=0.5×V _(tor)[ρ_(eff) u _(uff) ²−ρ₉₅₁ u ₉₅₁²]≈0.5×12.5×[1.1×184²−1.2×10²]≈232 kJ.To reach the dew-point temperature making the air portion saturated withhumidity, the circulating humid air portion of the volume V_(tor) mustlose the internal heat energy, indicated by AU, estimated as:ΔU=ρ _(eff) V _(tor) R(T ₉₅₁ −T _(dew))≈1.1×125×(8.31/0.0285)≈38 kJ.

The estimated value of the acquired kinetic energy K_(acquired) is muchgreater than the value of internal heat energy loss ΔU, so afterreaching the dew-point temperature, the energy difference(K_(acquired)−ΔU) 194 kJ goes to trigger the water condensation process.Condensation of water at the dew-point temperature requires a reducingof the saturated humid air portion's heat energy per unit mass on thevalue Λ_(water)=2260 kJ/kg. Thereby, the estimated acquired kineticenergy of airflow K_(acquired) potentially may be accompanied by thecondensed water amount of M_(water)=(K_(acquired)−ΔU)/Λ_(water)≈86 g.The value M_(water) is substantially lesser than the estimated abovemass M_(V) of water-vapor that potentially could be condensed, so thewater mass amount M_(water)≈86 g is actually feasible for condensation.

Further, a part of the circulating airflow can be permanently withdrawnin the form of outflowing jetstreams, for instance, under the influenceof wings 958, arranged adjacent to the elemental jet-boosters 950 toredirect circulating airflow portions 959, resulting in drawing out airportions 956, 954, and 955 from the imaginary toroidal space. Theoutflowing jetstreams take away the acquired kinetic energy ofcirculating airflow K_(acquired). As the accumulated kinetic energyK_(acc) of the airflow, circulating within the imaginary toroidal space,has a tendency to stabilization, so, an arisen lack of the accumulatedkinetic energy of airflow K_(acc), caused by the withdrawn of theacquired kinetic energy of airflow K_(acquired), has a tendency to bereacquired again by sucking fresh portions of the surrounding air intothe imaginary toroidal space and further, by an acceleration of thesucked fresh portions, increasing the sucked fresh portions localvelocity up to the stabilized effective local velocityu_(eff)=M*×u_(sound). The possible airflow discharge from and suckinginto the imaginary toroidal space, indicated by Q_(fresh), is defined bythe condition Q_(fresh)>A_(tor)u₉₅₁, as the ambient velocity u₉₅₁ issubstantially lower than the expected airflow local velocities at theborders of the imaginary toroidal space. Thus, the condition of thepossible airflow discharge Q_(fresh) is quantified as Q_(fresh)>1000m³/sec. The possible airflow discharge Q_(fresh) is much greater thanthe airflow F₉₅₇₃ moving through cross-section 9573 of the imaginarytoroidal space, estimated as F₉₅₇₃=0.25π×d₉₅₇₃ ²×u_(eff), and issufficient to refresh the humid air in the imaginary toroidal spacevolume V_(tor) several times per second, indicated by N_(refresh),defined and estimated as N_(refresh)=Q_(fresh)/V_(tor)>80 sec⁻¹N_(refresh)=Q_(fresh)/V_(tor)>80 sec⁻¹. The intensity of watercondensate harvesting, indicated by F_(condensation), is defined by thefeasible condensed water amount M_(water)≈86 g multiplied on theN_(refresh). Thus, the intensity of water condensate harvestingF_(condensation) is estimated as:

$F_{condensation} = {{N_{refresh} \times M_{water}} > {6.88\frac{kg}{\sec}} \approx {413\mspace{14mu}{kg}\text{/}{\min.}}}$The estimated intensity of water harvesting F_(condensation) is at leastof the same order of the value as a flux of water head discharging froma hose of a fire-extinguishing machine. Thereby, a stationarycircumferential arrangement of many elemental jet-boosters 950 can beused for water harvesting from air for domestic and industrial needs,and, for example, attached to a helicopter, can be adapted for afire-extinguishing.

In view of the foregoing description referring to FIG. 9f , it will beevident to a person skilled in the art that airfoil wings 958, exposedto stably-circulating airflow portions 959 and enabling rotations aroundthe vertical axis through point 957, may power a rotor of an electricitygenerator. Alternatively, the stabilized temperature difference betweenthe extra-cooled airflow portions, subjected to the triggered deLaval-like jet-effect, and the extra-warmed airflow portions, subjectedto the triggered de Laval-like retarding-effect, may be used to power aPeltier-element operating as thermoelectric generator producingelectricity, while the consumed heat power is restoring at the expenseof the surrounding air caloric entering the imaginary toroidal space.Thus, the acquired kinetic energy of airflow K_(acquired), refreshedN_(refresh) times per second, may provide an acquired kinetic-power ofairflow W_(acquired), defined as W_(acquired)=N_(refresh)×K_(acquired).Taking into the account the estimations made hereinabove, the possibleacquired kinetic-power of airflow W_(acquired) is estimated as:W_(acquired)>18.56 MW. Thereby, a relatively compact stationarycircumferential arrangement of many elemental jet-boosters 950 can beused for electrical power producing for domestic and industrial needs.

In view of the foregoing description referring to FIGS. 9a, 9b, 9c, 9d,9e, and 9f , it will be evident to a person skilled in the art that thecircumferential arrangement of many elemental jet-boosters exposed tomoving seawater can be adapted for electricity harvesting from theseawater motion.

In view of the foregoing description referring to FIGS. 9e and 9f , itwill be evident to a person skilled in the art that the circumferentialarrangement of many converging airfoil bodies operating as elementaljet-boosters 950 exposed to either natural or artificial wind can beused, for example, as a wind tunnel in an aerodynamic laboratory,providing a stable spatial distribution of the wind velocities.

In view of the foregoing description referring to FIGS. 9d, 9e, and 9f ,the inventor points out that, when the circumferential arrangement isregularly equidistant and when portions 955 and 956 are reaching thestabilized effective M-velocity equal to the value of the specificM-velocity M*=√{square root over ((γ−1)/γ)} near withers of thecircumferentially arranged elemental jet-boosters 950, the periodicallocal extra-accelerations and extra-retarding generate a forcedextra-intensive and in-phase superposed elemental acoustic waves,wherein the distance between each two neighbor withers equals a half ofwavelength of the forced extra-intensive elemental acoustic wave.

The inventor points out that each of elemental jet-boosters 950 acts asa source of an extra-intensive peculiar shock-like acoustic wavecharacterized by the peculiar frequency and wavelength, while each pairof the neighbor elemental jet-boosters 950 acts as a source of theextra-intensive forced elemental acoustic wave characterized by theforced frequency and wavelength. The forced extra-intensive elementalacoustic waves are superposed in-phase thereby constituting theresulting extra-intensive acoustic wave as constructive interferencewith respect to the system of coordinates linked to the whirling flowportions.

It will be evident to a person skilled in the art that thecircumferential arrangement of elemental jet-boosters 950, subjected tothe generalized jet-effect (namely, the Coanda-jet-effect, the deLaval-like jet-effect, the de Laval-like retarding effect, and theenhanced waving jet-effect) and supplied by an acoustic detector capableof detection of the resulting extra-intensive acoustic wave power, canplay a role of an electricity generator that, in the final analysis,produces the electrical power at the expense of the warmth of the air.

It will be evident to a person studied the present invention that thewhirling of air portion with the effective M-velocity equal to the valueof the specific M-velocity M*=√{square root over ((γ−1)/γ)} oncebecoming stabilized, continues self-supporting even in the absence ofthe circumferential arrangement of elemental jet-boosters 950. Forinstance, the well-known Great Red Spot of Jupiter is such a stabilizedtornado. Furthermore, constructive interference of extra-intensivepeculiar shock-like acoustic waves, characterized by the peculiarwavelength, can be observed as a regular polygon built-in into thestabilized whirling, where the side of the polygon is equal to thepeculiar wavelength. For instance, the well-known Saturn's Hexagon issuch a stabilized and stably whirling interference map.

Improved Wind-Turbine

FIG. 9g is a schematic drawing of modified improved wind-turbine 9.0,constructed according to the principles of the present invention tooperate under relatively fast airflow 9.1 for producing the electricalpower at the expense of the warmth of relatively fast airflow 9.1.

Modified improved wind-turbine 9.0 comprises:

-   -   axle 9.2 oriented along sagittal axis 9.21 codirected with fast        airflow 9.1,    -   identical asymmetrical biconvex actually-airfoil blades 9.3,        attached to axle 9.2; and    -   an engine [not shown here], capable of transforming the power of        the forced mechanic rotational motion 9.4 of axle 9.2 into the        electrical power.

The primary feature, making the modified wind-turbine 9.0 practicallyimplementable and extremely efficient, is the specifically configuredand so specifically functioning biconvex actually-airfoil blades 9.3.Namely, in contrast to standard wind-turbines having standardly shapedblades configured to be subjected to impacting by an incoming airflowthat, in particular, results in the airflow turbulence, retarding, andwarming, the modified improved wind-turbine 9.0 has asymmetricalbiconvex wing-like actually-airfoil blades 9.3:

-   -   having opposite convex sides 9.31 and 9.32 with withers        differing in convexity and    -   being oriented along and so adapted to the incoming fast airflow        jetstream 9.11 headway motion.        Thereby configured and oriented blades provide the so-called        zero attack angle:    -   to exclude or at least to minimize the impact by the incoming        fast airflow jetstream 9.11, but    -   to provide an interaction with the fast airflow jetstream 9.11        by the Coanda-jet-effect only, thereby resulting in an        acceleration and cooling of outflowing jetstream 9.6 and        resulting in lift-forces, acting on identical biconvex        actually-airfoil blades 9.3 and being disbalanced because of the        aligned asymmetry of the identical biconvex airfoil blades.        In this case, the axle 9.2 rotational motion, shown by the        curved arrow having numeral 9.4, is caused by the cumulative        resulting lift-force. Take note again, that the        Coanda-jet-effect is triggered by the airflow kinetic-power and        is actually powered at the expense of the airflow warmth but not        at the expense of the incoming fast airflow jetstream 9.11        kinetic-power; contrariwise, the kinetic-power of outflowing        jetstream 9.6 is increased or at least not decreased with        respect to the oncoming fast airflow 9.1. Thus, in contrast to        the standard wind-turbines, the proposed improved wind-turbine        9.0 is specifically characterized:    -   by the mechanism of operation, that is the Coanda-jet-effect but        not the impact; and    -   by the power source of operation, that is the warmth but not the        kinetic power of airflow.

Also, in contrast to a kind of the standard wind-turbines havingwing-like blades moving around a vertical axis, the proposed improvedwind-turbine 9.0 is specifically characterized by the excluding ofvarying poorly-streamlined positions of the wing-like blades.

As well, in contrast to the standard wind-turbines, a productivity ofthe proposed improved wind-turbine 9.0 is defined by the area of thebiconvex airfoil blades rather than by a so-called “swept area”, namely,the produced electrical power due to the Coanda-effect is specified asproportional to the biconvex airfoil blades area, i.e. the productivitycan be increased substantially for a given swept area.

In view of the foregoing description referring to FIG. 9g , it will beevident to a person skilled in the art that modified improvedwind-turbine 9.0 comprising:

-   -   the biconvex airfoil blades, having a wing-like sectional        contour with a longer so-called chord of wing, and/or    -   an increased quantity of the biconvex airfoil blades,        both circumstances provide for enforcing of the desired        Coanda-jet-effect. As well, it is self-suggested a sequential        in-line arrangement of a multiplicity of modified improved        wind-turbines 9.0 one downstream after another (optionally,        alternatingly differing in asymmetry to become forcedly rotated        alternatingly clockwise and inverse-clockwise, correspondingly),        each separately and all together efficiently operating within        the given swept area.

Moreover, at least one of the profiles 9.31 and 9.32 is implemented toprovide the de Laval enhanced jet-effect, when the incoming fast airflowjetstream 9.11 is flowing with a de Laval M-velocity and so a portion ofjetstream 9.11 is reaching the specific M-velocity nearby the withers ofthe asymmetrical biconvex actually-airfoil blades 9.3. In this case, theextra-efficiency of the modified improved wind-turbine is expected.

Furthermore, optionally, sides 9.31 and 9.32 differ in shape such thatone of the sides has one convex withers and the opposite side has atwo-humped airfoil profile providing for the two-stage operation of theCoanda-jet-effect as described hereinabove with the reference to FIG. 8d. Such asymmetrical blades, when exposed to oncoming fast airflow 9.1moving with a high M-velocity, higher than the specific M-velocity,become subjected, on the one hand, to the de Laval retarding effect, andon the other hand, to the de Laval enhanced jet-effect. This providesfor extra-increased lift-forces rotating axle 9.2. In this case, theextra-efficiency of the modified improved wind-turbine is expected in awide range of velocities.

FIG. 9h is a schematic drawing comprising the side view and front viewof an improved wind-turbine 9.7, constructed according to the principlesof the present invention to operate under relatively fast airflow 9.70for producing the electrical power at the expense of the warmth ofrelatively fast airflow 9.70. In relation to all the principal features,the improved wind-turbine 9.7 is similar to the improved wind-turbine9.0, described hereinabove referring to FIG. 9g , but now, referring tothe aforementioned optional diversity of the principal featuresimplementation, the biconvex actually-airfoil blades, which havingopposite at least partially convex sides 9.71 and 9.72 with withersdiffering in convexity, are further curved and screwed to optimize asuppression of turbulences as well as are cascaded one downstream afteranother to provide a multi-stage repeated operation of theCoanda-jet-effect thereby contributing to the desired cumulativelift-force to rotate axle 9.73.

In view of the foregoing description referring to FIGS. 9g and 9h , itwill be evident to a person skilled in the art that modified improvedwind-turbine 9.0 or 9.7, when attached to a flying aircraft, is capablefor efficient harvesting of the electrical power from the ambient airwarmth.

Furthermore, in view of the description expound hereinabove withreferences to FIGS. 5i, 5j, 5k, 9a, 9b, 9c, 9d, 9e, and 9f , theinventor points out that the mentioned multiplicity of modified improvedwind-turbines 9.0 or 9.7, arranged sequentially one downstream afteranother [not shown here], results in generation of acoustic wavesaccompanied by extraction of the internal heat energy of ambient air infavor for the wave power due to the enhanced waving jet-effect. Thus, asystem, comprising the arrangement and a detector of the acquired wavepower, has an additional degree of freedom to increase the efficacy ofthe producing of electricity.

In view of the foregoing description referring to FIGS. 9g and 9h incombination with the foregoing description of subparagraphs “Point ofSail” and “Flying Bird”, both with the reference to prior art FIG. 1i ,it will be evident to a person skilled in the art that the constructionof modified improved wind-turbine 9.7, when having a controllable speedof the axle 9.73 rotation adapted to the velocity of oncoming airflow9.70 to keep the airflow remaining laminar, provides a controllable netjet-thrust against the oncoming airflow 9.70 and so becomes applicableas a kind of jet-engine for a controllable and substantially noiselessflying.

A Jet-Transformer

FIG. 9i is a schematic illustration of a concept to transform theambient warmth into electricity. The concept is embodied as ajet-transformer 9.80 comprising:

-   -   a vertically oriented specifically shaped pipe 9.81 having the        optimized convergent-divergent inner tunnel, described        hereinabove in sub-paragraph “Convergent-Divergent Jet-Nozzle”        with reference to FIG. 6 a,    -   at least one laminar flow maker 9.82, conceptually, having a        geometry of convex-concave corpus 9.821 supplied by a heater        9.822, i.e. being designed as the convex-concave corpus 512        described hereinabove with reference to FIG. 5e , and    -   at least one improved wind-turbine 9.83, designed as the        improved wind-turbine 9.7 described hereinabove referring to        FIG. 9 h,        the all, constructed according to the principles of the present        invention.

The specifically shaped pipe 9.81 is elevated above the ground to allowfor the ambient air 9.841 entering the optimized convergent-divergentinner tunnel from below. The heater 9.822 supplies the heat energy to afluid portion adjacent the focus of the parabolically-concave surface9.823 of the convex-concave corpus 9.821, thereby, on the one hand, totrigger the Archimedes upward-vectored buoyant force lifting the heatedfluid portion and, on the other hand, to align the airflow 9.842 upwardalong the vertical axis 9.851. The upward airflow 9.842 is relativelyslow and substantially-laminar. The optimized convergent-divergent innertunnel is designed according to the equation of principle (6.13) toprovide for a substantial suppression of jumps of the air thermodynamicparameters and, thereby, to provide for the substantial acceleration ofthe airflow 9.842, laminarly and so noseless streaming upward. So, theheating triggers the upward motion of air, and, in turn, the fluidmotion itself triggers the convective acceleration as the airflow movesthrough the narrowing cross-section of the optimizedconvergent-divergent inner tunnel.

Considering:

-   -   the ambient temperature above the exhaust 9.854 equal T_(e),    -   the temperature near the level 9.852 equal T₀, and    -   the temperature near the narrow throat 9.853 equal T*,        equation (7.1c), described hereinabove referring to FIG. 7a ,        says that:    -   on the one hand, to obtain the de Laval jet-effect for air        utilizing the optimized convergent-divergent inner, one must        provide the ratio T₀/T, at least of 1.2; and    -   on the other hand, to accelerate an air portion up to the        velocity of sound, one must provide the ratio T₀/T_(e) at least        of 1.7.

Hence, providing the heating of air near the level 9.852 up to about thetemperature 234° C. only, the condition of the enhanced de Lavaljet-effect becomes satisfied, in turn, providing that the relatively lowheat power, supplied by heaters 9.822, triggers the enhanced de Lavaljet-effect transforming the warmth of the moving airflow into theacquired kinetic power of the airflow.

The energy E₀, necessary for warming 1 cube meter of air from thetemperature 25° C. up to the temperature 234° C., is estimated asE₀=ρVC_(V)(T₀−T_(e)), where V is the volume of 1 cube meter, ρ is theair density, ρ≈1.2 kg/m³, C_(V) is the air heat capacity, C_(V)≈0.72kJ/(kg·K), thereby, E₀≈1.2×1×0.72×(234−25)≈180 kJ.

As the mentioned assumed condition allows to accelerate the airflowportion 9.854 up to the specific M-velocity M*=√{square root over((γ−1)/γ)} near the narrow throat 9.853 and to accelerate the airflowportion 9.854 up to almost the speed of sound (i.e. the exhaustM-velocity is of M_(e)≈1), then:

-   -   the acquired kinetic energy, K_(e), of the outflowing airflow        portion 9.854, which (the acquired kinetic energy K_(e)) is        specified as the difference between bringing heat energies,        equals K_(e)≈n×(T₀−T_(e))×R, where n is number of moles in the        considered 1 cube meter of air, n≈44.64, and R is the specific        gas constant, approximated for the air by R=287 J/(kg·K), i.e.        K_(e) 44.64×209×287≈2,677 kJ, that, in turn, says that the        acquired kinetic energy K_(e) may exceed the consumed energy E₀        at least at subsonic velocities by the factor of 15; and    -   the acquired kinetic energy, K*, of the airflow portion 9.854,        when crossing the narrow throat, equals K*≈n×(T₀−T*)×R≈764 kJ,        thereby showing that the acquired kinetic energy K* may exceed        the consumed energy E₀ by the factor of 4.24.

It will be evident to a commonly educated person that, if not to use theoptimized convergent-divergent inner tunnel, designed according to theequation of principle (6.13), the mentioned effective conversion of theairflow heat energy into the airflow kinetic energy is impossiblebecause of originated turbulences and Mach waves, both accompanied bynoise and energy dissipation back to the air warmth.

The improved wind-turbine 9.83 meets the upping laminar airflow andprovides for a production of electricity neither retarding the upwardairflow and nor distorting the upward airflow laminarity as describedhereinabove referring to FIGS. 9g and 9h . The inventor points out againthat the improved wind-turbine 9.83 harvests electrical power at theexpense of the airflow warmth but not from the airflow kinetic power,wherein the increased kinetic power of the airflow plays the role of anenforced trigger of the lift-force rotating the improved wind-turbine.Moreover, optionally, in-line arranged several improved wind-turbines9.83 provide for a multi-stage repeatedly harvesting of electricity fromthe same airflow portion.

Method for Computational Analysis

FIG. 10 is a schematic block-diagram 1000 of a method for computationalfluid dynamics numerical analysis, based on the principles of thepresent invention.

Block 1010 represents standard pre-processing comprising a defining thecalculation space and mesh for the space quantization.

Block 1020 represents the processing itself, i.e. the algorithmcalculating numerically the spatial distribution of the velocity-vector(three components), static pressure, temperature, and density (total sixcomponents), programmed according to the principles of the presentinvention, and applying a computational analysis basic principle,comprising a digital approximation of a space, comprising the flowingfluid, by a virtual spatial mesh partitioned into non-overlappingquantization cells bordered by imaginary boundaries.

The processing is such that the calculated spatially distributed valuesare satisfied, on the one hand, to suggested modified equations of fluidmotion (5.6), (5.7), (5.9) having an exact solution, and, on the otherhand, to the gravitational, thermodynamic, and kinetic theory lawsrepresented by specified equations (5.2), (5.3), (5.4), (5.5), and(5.8), wherein the adequacy of the solution is confirmed by theBernoulli theorem, equation (5.10).

Block 1030 represents the standard post-processing procedure for thesolution filing and visualization.

Thereby, one can implement blocks 1010, 1020, and 1030 as a computerprogram product comprising a computer usable medium having computerreadable code and instructions embodied and stored therein for executionon a general purpose computer. The code and instructions, when executedby the computer, cause the computer to perform the method forcomputational fluid dynamics.

FIG. 11 comprises Table-1 showing several equations:

-   -   On the one hand, classical, derived from the Euler theory in        frames of the continuum mechanics and thermodynamics; and    -   On the other hand, specified in the present invention, derived        basing on the principles of the kinetic theory of matter.

The inventor points out that:

-   -   The difference between the expressions of the equations of fluid        motion: classical and specified, is predetermined by the        difference of definitions of the inner static pressure and        density. Namely, in the continuum mechanics, the static pressure        is defined as an integrated mechanical parameter characterizing        the force acting on a wall, wherein the static pressure and mass        density are inter-independent; and, in the present invention,        the interrelated inner static pressure and mass density, both        are defined from the point of view of the kinetic theory of        matter applied to molecular fluid;    -   The generalized adiabatic compressibility parameter, indicated        by γ, generalizes the adiabatic compressibility-constant,        indicated by j, by taking into the consideration that the        adiabatic compressibility properties are predetermined by both:        the adiabatic compressibility-constant and the van der Waals        constants;    -   The equation of principle (6.13) differs from the classical        equation (1) derived basing on the Euler equation defined in        frames of the continuum mechanics; and    -   The specific M-velocity M*=√{square root over ((γ−1)/γ)} differs        from the M-velocity of 1 Mach, which plays the role of the        specific M-velocity in the classical aerodynamic theory of the        de Laval nozzle.

The method, based on the kinetic theory of matter, provides the modifiedequations of fluid motion, thereby, reducing a sense of one of theMillennium Goals to solve the problem of the Navier-Stokes equationsolution existence.

Considering a fluid as a substance composed of randomly movingmolecules, the method enables applications optimization, the physicalessence of which is to bring in an asymmetrical influence into themolecular fluid, and, thereby, to originate a motion of molecules in aprevalent direction. For instance, such an asymmetry is provided by astructured and heated surface thereby repelling the molecular fluid in aprevalent direction, or by a structured naturally hydrophobic surfacecontacting with water, or by a structured and electrically chargedsurface interacting with an ionized fluid, or by an airfoil body movingrelative to the molecular fluid and thereby acting on the molecularfluid by the Coanda-effect.

The method enables optimized designs of apparatuses for electricityharvesting from the molecular fluid heat energy, providing a positivenet-efficiency. The method, accompanied by novel teachings, allows foroptimized designs of engines having novel functionalities, for examples,such as:

-   -   Fluid-repellent jet-gears, described with references to FIGS.        5d, 5e, 5f, 5g, 5h, 5i, 5j, and 5k , which, when submerged in        ambient fluid, originate a circulating and/or headway        self-motion at the expense of the ambient fluid warmth; as well,        creating a controllable omniphobic repellency using heating        elements, one can originate a fluid-repellent jet-gear motion        with a high net-efficiency, even higher than 100%, again, at the        expense of the ambient fluid warmth;    -   An ice-maker comprising either hydrophobic jet-gears and        comprising a generator, in the final analysis, transforming the        heat into electricity, and thereby cooling and freezing water        and so harvesting potable water (i.e. ice), as described with        references to FIG. 5 g;    -   A capillary tube having inner saw-like hydrophobic walls,        described with reference to FIG. 5d , which, when filled with        water, provides the water transportation;    -   Referring to FIG. 5i comprising a spiral, having a form of the        Archimedean screw and having a hydrophobic surface, a mechanism,        synthesizing a natural protein, or more fundamentally, of        ribonucleic acid (RNA) molecules, hypothetically, can be        specified and implemented artificially;    -   An electrically charged propeller-like jet-gear, described with        references to FIG. 5h , which, when submerged in an ionized gas        or liquid, provides a motion of the jet-gear at the expense of        the ionized fluid's warmth;    -   A motionless gravity-jet engine, described with references to        FIG. 5m , which, when operating in the gravitational field, is        capable of a transformation of water heat energy into the        kinetic energy of water jetstream moving upward, which, when        becomes reincarnated into a waterfall, allows for the        electricity harvesting and wherein reverting a falling water        portion back into a container;    -   A generalized generator for producing a useful-beneficial power,        described with reference to FIG. 5l , which,        -   when concretized as a fluid flow accelerator, provides for            the useful-beneficial power harvesting from the fluid warmth            in an adiabatic process due to the Coanda-jet-effect; and        -   when concretized as a waves synchronizer, provides for the            useful-beneficial power harvesting using constructive            interference due to the waving jet-effect;    -   An optimized convergent-divergent tunnel, described with        reference to FIG. 6a , which, when triggering the de Laval        enhanced jet-effect, provides conditions to acquire a kinetic        power and/or to harvest electricity from air warmth with a        positive net-efficiency;    -   A two-stage convergent-divergent jet-nozzle described with        reference to FIG. 6h , which, when exposed to transonic and/or        supersonic and/or hypersonic flow, in contrast to the known        phenomenon of the incoming flow warming and retarding, provides        the incoming flow cooling and acceleration;    -   An airfoil flying capsule having an optimized single-stage or        two-stage convergent-divergent tunnel, which, when moving in        air, is capable of transforming the air warmness into a useful        jet-thrust;    -   An improved propeller, preferably composed of many small        propellers distributed in space, which focuses and/or defocuses        sub-portions of air, thereby forming a cumulative blowing and/or        sucking jetstream, correspondingly, wherein the jetstream has an        optimally-variable cross-section providing for the critical        condition, triggering the de Laval-like enhanced jet-effect;    -   An improved wind-turbine configured:        -   to exclude or at least to minimize the impact by incoming            airflow, but        -   to trigger at least one of the Coanda-effect and the de            Laval enhanced jet-effect, both having the jet-effect            nature, and, in the final analysis,        -   to produce the electrical power at the expense of the            airflow warmth but not at the expense of the airflow            kinetic-power;    -   and    -   An adiabatic aerodynamic system described with reference to        FIGS. 9e and 9f , comprising a stationary circumferential        arrangement of many elemental jet-boosters, that is capable of        acquiring the kinetic energy of circulating airflow at the        expense of the ambient air heat energy, further, to accumulate        and conserve the airflow kinetic energy in a form of        stably-circulating airflow. Wherein the adiabatic aerodynamic        system, exposed to the natural ambient wind, accumulates and        conserves the kinetic energy of the stably-circulating airflow        independently of weather conditions, namely, independently of        the direction of horizontal wind, as well as independently of        any variation in the natural gusty wind direction, and        furthermore, independently of any variation of the natural gusty        wind non-zero velocity. This provides at least the following        novel applications:        -   The adiabatic aerodynamic system can operate as            vortex-generator of an electro-station, providing for            electrical power harvesting from the warmth of natural air.            Furthermore, it is found that the adiabatic aerodynamic            system exposed to an artificial wind, made by consuming            either a power of burned fuel or an electrical power, under            certain conditions, can convectively accelerate the wind at            the expense of the airflow warmth thereby providing an            acquired kinetic power of airflow being higher than the            power consumed for the making of artificial wind;        -   The adiabatic aerodynamic system can be used as engine,            powering a flying-saucer of high mobility, wherein, in            contrast to a principle of helicopter where rotating            wing-like blades interact with stationary air, here, just            stationary wings of the flying-saucer interact with the            stably-circulating airflow;        -   The adiabatic aerodynamic system can be adapted for a            condensation of natural air humidity, wherein, considering a            relatively compact adiabatic aerodynamic system, an            estimated intensity of the water harvesting is at least of            the same order of the value as a flux of water head            discharging from a hose of a fire-extinguishing machine; and        -   The adiabatic aerodynamic system, made in large-scale, can            be used as a windbreak of an oasis of a stably-eddying            windiness and refreshing coolness.

The method enables a technology to control the transformation of theambient surroundings (for instance, air and/or water) warmth into adirectional motion of the fluid providing for a renewable cycle,comprising:

-   -   transformation of the flowing fluid heat-power into acquired        kinetic-power of an originated jetstream;    -   conversion of the jetstream kinetic-power into useful        electric-power; and    -   consumption of the electric-power, in the final analysis,        inevitably dissipating back into the warmth of surrounding        matter.

The method, accompanied by novel teachings, allows for a proper analysisof waves as a process of an interaction between an oscillator, supplyingpower to the ambient medium, and the ambient medium itself; wherein theprocess is accompanied by an adiabatic process of the waves propagationand interference.

The method enables optimized designs of controllable apparatuses havingnovel functionalities for a useful-beneficial power harvesting (forinstance, a harvesting of electricity from the molecular fluid heatenergy using constructive interference of energeticallyinter-independent acoustic waves). Furthermore, applications, providingfor a use of constructive interference of acoustic waves, arehypothetically translatable to applications, providing for a use ofconstructive interference of electromagnetic waves.

DRAWINGS

It should be understood that the sketched exemplary embodiments aremerely for purposes of illustrating the teachings of the presentinvention and should in no way be used to unnecessarily narrow theinterpretation of, or be construed as, being exclusively definitive ofthe scope of the claims which follow.

It is anticipated that one of skill in the art will make manyalterations, re-combinations, and modifications of the embodimentstaught herein without departing from the spirit and scope of the claims.

I claim:
 1. A corpus of a fluid-repellent jet-gear, submerged in ambientfluid; wherein a phobic-repulsing jet-effect is defined as a kind ofjet-effect, occurring in a fluid near to a surface made from afluid-repellent material; wherein said kind of jet-effect occurring,when nearby fluid portions, contacting with the surface, becomesubstantially subjected to a repelling action of phobic-repulsive vander Waals forces originated by the fluid-repellent material, whereinsaid repelling action being appeared as both a first acceleration of thenearby fluid portions relative to said corpus of the fluid-repellentjet-gear and a second acceleration of the nearby fluid portions relativeto ambient fluid portions yet to be subjected to said phobic-repulsingjet-effect; both said first and second accelerations occurring at theexpense of said nearby and ambient fluid portions' internal heat energy,the phobic-repulsing jet-effect is further specified by a diversity ofmechanisms resulting in the repelling action of phobic-repulsive van derWaals forces originated by the fluid-repellent material; the diversityof the mechanisms is at least one of: an electrically charged surfacesubmerged in ionized gas or liquid functions as a fluid-repellentmaterial; a magnetic surface, submerged in a diamagnetic liquid,functions as a fluid-repellent material repelling the diamagneticliquid; wherein said fluid-repellent jet-gear corpus comprising asurface layer, made from a fluid-repellent material; wherein saidsurface layer having two portions: first and second, of arelief-structured surface, differing in fluid-repelling property andcontacting with nearby portions of said fluid to provide that saidnearby fluid portions contacting with at least said first portion of thefluid-repellent relief-structured surface become subjected to arepelling action of phobic-repulsive van der Waals forces originated bythe fluid-repellent material, wherein said repelling action of thephobic-repulsive van der Waals forces being an uncompensated action onsaid nearby fluid portions to result in an acceleration of the nearbyfluid portions; wherein said two portions: first and second, of thefluid-repellent relief-structured surface comprising airfoilprotrusions, being shaped, arranged, and oriented asymmetrically fromthe point of view of directivity of the repelling action, therebyproviding a cumulative repelling action of said phobic-repulsive van derWaals forces on said nearby fluid portions in unison and co-oriented ina prevalent direction, thereby causing said nearby fluid portions motionin said prevalent direction; wherein said asymmetrically shaped andoriented two portions: first and second, of the fluid-repellentrelief-structured surface of said airfoil protrusions having a form ofat least one of saw-like airfoil curved teeth, curved cogs havingconcave sides with parabolic sectional profiles, airfoil curvedteeth-like fins, fish-scales having airfoil overall; wherein an overallconfiguration of said fluid-repellent jet-gear corpus having asubstantially-airfoil orientation, aligned to said prevalent direction;thereby, said asymmetrically shaped and oriented two portions: first andsecond, of the fluid-repellent relief-structured surface of said airfoilprotrusions provide airfoil streamlines of said nearby fluid portionsmoving in said prevalent direction; wherein said asymmetrically shapedand oriented two portions: first and second, of the fluid-repellentrelief-structured surface of said airfoil protrusions are stationaryrelative to said fluid-repellent jet-gear corpus; wherein said overallconfiguration of said fluid-repellent jet-gear corpus is in a form of awheel, shaped as circle-saw, having said saw-like airfoil curved teethand said substantially-airfoil orientation being clockwise orinverse-clockwise, wherein said prevalent direction of said nearby fluidportions motion, being at least partially whirling, wherein saidfluid-repellent jet-gear corpus is: stationary relative to said ambientfluid's portions, yet to be subjected to a phobic-repulsing jet-effect,or rotating within a portion of space, thereby moving relative to saidambient fluid's portions yet to be subjected to a phobic-repulsingjet-effect; wherein said fluid is at least one of a water-based liquid,an oil-based liquid, an alcohol-based liquid, and an ionized gas orliquid.
 2. The corpus of a fluid-repellent jet-gear of claim 1, wherein:said fluid is diamagnetic; and the first portion of the fluid-repellentrelief-structured surface of said airfoil protrusions is embodied as apermanent magnet.
 3. The corpus of a fluid-repellent jet-gear of claim1, wherein: said fluid is plasma or electrolyte or ionized gas; and thefirst portion of the fluid-repellent relief-structured surface of saidairfoil protrusions is embodied as a fluid-repellent charged surface. 4.The corpus of a fluid-repellent jet-gear of claim 1, wherein the firstportion of the fluid-repellent relief-structured surface of said airfoilprotrusions is hotter than said ambient fluid.